Qing Liu

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An efficient and truthful pricing mechanism for team formation in crowdsourcing markets

2015-06-01

Qing Liu , Tie Luo , Ruiming Tang +1 more

In a crowdsourcing market, a requester is looking to form a team of workers to perform a complex task that requires a variety of skills. Candidate workers advertise their certified … In a crowdsourcing market, a requester is looking to form a team of workers to perform a complex task that requires a variety of skills. Candidate workers advertise their certified skills and bid prices for their participation. We design four incentive mechanisms for selecting workers to form a valid team (that can complete the task) and determining each individual worker's payment. We examine profitability, individual rationality, computational efficiency, and truthfulness for each of the four mechanisms. Our analysis shows that TruTeam, one of the four mechanisms, is superior to the others, particularly due to its computational efficiency and truthfulness. Our extensive simulations confirm the analysis and demonstrate that TruTeam is an efficient and truthful pricing mechanism for team formation in crowdsourcing markets.

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On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group

2013-06-10

Fausto Ferrari , Qing Liu , Juan J. Manfredi

We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set … We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group.

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On the characterization of $p$-harmonic functions on the Heisenberg group by mean value properties

2013-12-10

Fausto Ferrari , Qing Liu , Juan J. Manfredi

We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1 < p <\infty$, following the schemedescribed in [16] for the Euclidean case. … We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1 < p <\infty$, following the schemedescribed in [16] for the Euclidean case. The new tool that allows us to consider the subelliptic case is a geometric lemma, Lemma 3.2 below, that relates the directions of the points of maxima and minima of a function on a small subelliptic ball with the unit horizontal gradient of that function.

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General existence of solutions to dynamic programming equations

2014-09-01

Qing Liu , Armin Schikorra

We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, … We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, mean curvature flow and Hamilton-Jacobi type. Our general result is similar to Perron's method but adapted to the discrete situation.

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Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton–Jacobi equations with noncoercive Hamiltonians

2011-11-08

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations

2013-09-04

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

We investigate the large-time behavior of viscosity solutions of Hamilton-Jacobi equations with noncoercive Hamiltonian in a multidimensional Euclidean space. Our motivation comes from a model describing growing faceted crystals recently … We investigate the large-time behavior of viscosity solutions of Hamilton-Jacobi equations with noncoercive Hamiltonian in a multidimensional Euclidean space. Our motivation comes from a model describing growing faceted crystals recently discussed by E. Yokoyama, Y. Giga and P. Rybka. Surprisingly, growth rates of viscosity solutions of these equations depend on the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding="application/x-tex">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-variable. In a part of the space called the <italic>effective domain</italic>, growth rates are constant, but outside of this domain, they seem to be unstable. Moreover, on the boundary of the effective domain, the gradient with respect to the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding="application/x-tex">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-variable of solutions blows up as time goes to infinity. Therefore, we are naturally led to study singular Neumann problems for stationary Hamilton-Jacobi equations. We establish the existence, stability and comparison results for singular Neumann problems and apply the results for a large-time asymptotic profile on the effective domain of viscosity solutions of Hamilton-Jacobi equations with noncoercive Hamiltonian.

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A game-theoretic proof of convexity preserving properties for motion by curvature

2016-01-01

Qing Liu , Armin Schikorra , Xiaodan Zhou

Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group

2016-06-22

Qing Liu , Juan J. Manfredi , Xiaodan Zhou

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On a discrete scheme for time fractional fully nonlinear evolution equations

2019-11-01

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo’s time fractional derivatives. We prove the convergence of the scheme in the framework of the theory … We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo’s time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can be viewed as a resolvent-type approximation.

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Fattening and Comparison Principle for Level-Set Equations of Mean Curvature Type

2011-01-01

Qing Liu

In this paper, we give several applications of the discrete game approach to partial differential equations (PDEs). We first present a rigorous game-theoretic proof of fattening phenomenon for motion by … In this paper, we give several applications of the discrete game approach to partial differential equations (PDEs). We first present a rigorous game-theoretic proof of fattening phenomenon for motion by curvature with figure-eight–shaped initial curves without using parabolic PDE theory. The proof is based on a comparison between the game value and its inverse. Accompanied by the example of figure eight, our second result shows, for the stationary equation of mean curvature type in an arbitrary region $\Omega$, that fattening of positive curvature flow with initial surface $\partial\Omega$ causes loss of the weak comparison principle, which partially answers an open question posed by Kohn and Serfaty in 2006. In addition, we prove the existence of solutions of the stationary problem and its game approximation in the absence of comparison principles but under regularity conditions of the flow. The main difference between our games and those in other papers is that we take the domain perturbation into consideration.

Existence and Symmetry of Ground States to the Boussinesq abcd Systems

2014-11-18

Ellen Shiting Bao , Robin Ming Chen , Qing Liu

Equivalence of solutions of eikonal equation in metric spaces

2020-10-21

Qing Liu , Nageswari Shanmugalingam , Xiaodan Zhou

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Waiting time effect for motion by positive second derivatives and applications

2013-12-30

Qing Liu

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Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces

2018-11-01

Qing Liu , Atsushi Nakayasu

We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we show that in a Busemann … We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we show that in a Busemann space the unique metric viscosity solution preserves the geodesic convexity of the initial value at any time. We provide two approaches and also discuss several generalizations for more general geodesic spaces including the lattice grid.

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Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations

2019-12-09

Kazuhiro Ishige , Qing Liu , Paolo Salani

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A Remark on the Discrete Deterministic Game Approach for Curvature Flow Equations

2008-01-01

Yoshikazu Giga , Qing Liu

This paper constructs a family of discrete two-person games, whose values converge to the unique viscosity solution of a general curvature flow equation in dimension two. We summarize all of … This paper constructs a family of discrete two-person games, whose values converge to the unique viscosity solution of a general curvature flow equation in dimension two. We summarize all of the techniques needed for such second-order games. We introduce barrier games, which can be considered as a combination of the classical barrier argument and game perspectives.

A nonlinear parabolic equation with discontinuity in the highest order and applications

2015-09-24

Robin Ming Chen , Qing Liu

An obstacle problem arising in large exponent limit of power mean curvature flow equation

2018-10-15

Qing Liu , Naoki Yamada

We study limit behavior for the level-set power mean curvature flow equation as the exponent tends to infinity. Under Lipschitz continuity, quasiconvexity, and coercivity of the initial condition, we show … We study limit behavior for the level-set power mean curvature flow equation as the exponent tends to infinity. Under Lipschitz continuity, quasiconvexity, and coercivity of the initial condition, we show that the limit of the viscosity solutions can be characterized as the minimal supersolution of an obstacle problem involving the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding="application/x-tex">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Laplacian. Such behavior is closely related to applications of power mean curvature flow in image denoising. We also discuss analogous behavior for other evolution equations with related applications.

A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions

2019-12-09

Nao Hamamuki , Qing Liu

This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition … This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition for general parabolic or elliptic equations can be generated by including reflections on the boundary to the interior optimal control or game interpretations. We study a dynamic version of such type of boundary problems, generalizing the discrete game-theoretic approach proposed by Kohn-Serfaty (2006, 2010) for Cauchy problems and later developed by Giga-Liu (2009) and Daniel (2013) for Neumann type boundary problems.

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Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations

2021-02-10

Qing Liu , Xiaodan Zhou

This paper introduces in a natural way a notion of horizontal convex envelopes of continuous functions in the Heisenberg group.We provide a convexification process to find the envelope in a … This paper introduces in a natural way a notion of horizontal convex envelopes of continuous functions in the Heisenberg group.We provide a convexification process to find the envelope in a constructive manner.We also apply the convexification process to show h-convexity of viscosity solutions to a class of fully nonlinear elliptic equations in the Heisenberg group satisfying a certain symmetry condition.Our examples show that in general one cannot expect h-convexity of solutions without the symmetry condition.

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The vanishing exponent limit for motion by a power of mean curvature

2020-04-15

Qing Liu

We discuss limit behavior of solutions to level set equation of power mean curvature flow as the exponent tends to zero, which has important applications to shape analysis in image … We discuss limit behavior of solutions to level set equation of power mean curvature flow as the exponent tends to zero, which has important applications to shape analysis in image processing. A formal limit yields a fully nonlinear singular equation that describes the motion of a surface by the sign of its mean curvature.We justify the convergence by providing a definition of viscosity solutions to the limit equation and establishing a comparison principle.

A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications

2021-03-24

Nao Hamamuki , Qing Liu

Abstract This paper is devoted to a game-theoretic approach to the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under the comparison principle for the dynamic boundary problem, we … Abstract This paper is devoted to a game-theoretic approach to the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under the comparison principle for the dynamic boundary problem, we construct a family of deterministic discrete games, whose value functions approximate the unique viscosity solution. We also apply the game approximation to study the convexity preserving properties and the fattening phenomenon for this geometric dynamic boundary problem.

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Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations

2022-12-12

Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

Abstract This paper is concerned with a general class of fully nonlinear parabolic equations with monotone nonlocal terms. We investigate the quasiconvexity preserving property of positive, spatially coercive viscosity solutions. … Abstract This paper is concerned with a general class of fully nonlinear parabolic equations with monotone nonlocal terms. We investigate the quasiconvexity preserving property of positive, spatially coercive viscosity solutions. We prove that if the initial value is quasiconvex, the viscosity solution to the Cauchy problem stays quasiconvex in space for all time. Our proof can be regarded as a limit version of that for power convexity preservation as the exponent tends to infinity. We also present several concrete examples to show applications of our result.

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THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS

2013-12-13

Qing Liu , Tiantian Mao , Taizhong Hu

Let X 1 , …, X n be non-negative, independent and identically distributed random variables with a common distribution function F , and denote by X 1: n ≤ ··· … Let X 1 , …, X n be non-negative, independent and identically distributed random variables with a common distribution function F , and denote by X 1: n ≤ ··· ≤ X n:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of X k:n and X j:n − X i:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n .

On a discrete scheme for time fractional fully nonlinear evolution equations

2019-02-23

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory … We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can be viewed as a resolvent-type approximation.

Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games

2021-01-01

Qing Liu

Singular Neumann Boundary Problems for a Class of Fully Nonlinear Parabolic Equations in One Dimension

2021-01-01

Takashi Kagaya , Qing Liu

In this paper, we discuss a singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes the motion of a planar … In this paper, we discuss a singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes the motion of a planar curve sliding along the boundary with a zero contact angle, which can be viewed as a limiting model for the capillary phenomenon. We study the uniqueness and existence of solutions by using the viscosity solution theory. We also show the convergence of the solution to a traveling wave as time proceeds to infinity when the initial value is assumed to be convex.

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Discontinuous eikonal equations in metric measure spaces

2024-08-07

Qing Liu , Nageswari Shanmugalingam , Xiaodan Zhou

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of … We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these.For toral subgroups, we give an effective classification algorithm.For non-toral elementary abelian subgroups, we focus on algebraic groups of exceptional type with a view to future applications, and in this case we provide tables explicitly describing the subgroups and their local structure.We then describe how to transfer results to the corresponding finite groups of Lie type using the Lang-Steinberg Theorem; this will be used in forthcoming work to complete the classification of elementary abelian p-subgroups for torsion primes p in finite groups of exceptional Lie type.Such classification results are important for determining the maximal p-local subgroups and p-radical subgroups, both of which play a crucial role in modular representation theory.

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Phase 2/3 Trials

2014-09-29

Qing Liu

Abstract Seamless phase 2/3 combination designs (or phase 2/3 designs) hold great promise to bring optimal treatment to patients early and more efficiently. The concept is to combine traditional phase … Abstract Seamless phase 2/3 combination designs (or phase 2/3 designs) hold great promise to bring optimal treatment to patients early and more efficiently. The concept is to combine traditional phase 2 and phase 3 trials seamlessly in operation and inferentially in statistical analysis. As phase 2/3 designs cover a large area of clinical applications, it is not possible to provide comprehensive details for all different clinical applications in this article. Rather, the focus is on providing general descriptions of phase 2/3 designs and their legal foundations under the framework of Title 21 Part 312 of Code of Federal Regulations and Section 355 (b) of the Federal Food, Drug, and Cosmetic Act. This legal framework also provides the basis for correcting misrepresentations of phase 2/3 combination designs found in the literature. Various aspects and underlying principles are discussed in depth with highlights on current difficulties and future challenges to statistical inference.

Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group

2018-05-04

Qing Liu , Xiaodan Zhou

Large exponent behavior for power-type nonlinear evolution equations and applications

2019-09-24

Qing Liu

On game interpretations for the curvature flow equation and its boundary problems (パターンダイナミクスの数理とその周辺--RIMS研究集会報告集)

2009-04-01

Qing Liu

Discontinuous eikonal equations in metric measure spaces

2023-01-01

Qing Liu , Nageswari Shanmugalingam , Xiaodan Zhou

In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a … In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is known that the notion of Monge solutions is equivalent to the standard definition of viscosity solutions. Generalizing the notion of Monge solutions in our setting, we establish uniqueness and existence results for the associated Dirichlet boundary problem. The key in our approach is to adopt a new metric, based on the optimal control interpretation, which integrates the discontinuous term and converts the eikonal equation to a standard continuous form. We also discuss the Holder continuity of the unique solution with respect to the original metric under regularity assumptions on the space and the inhomogeneous term.

Hamilton-Jacobi equations in metric spaces

2023-01-01

Qing Liu , Xiaodan Zhou

These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few important … These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few important results concerning the well-posedness of Hamilton-Jacobi equations in metric spaces, especially several recently proposed notions of metric viscosity solutions to the eikonal equation. Basic knowledge about metric spaces and a review of viscosity solution theory in the Euclidean spaces are also presented.

A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications

2023-01-01

Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a … This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a control-based representation formula for solutions. We also apply the formula to discuss the fattening phenomenon and large-time asymptotics of the solutions.

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A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality

2024-05-26

Kazuhiro Ishige , Qing Liu , Paolo Salani

In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality and properties of diffusion equations of … In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality and properties of diffusion equations of porous medium type pertaining to the large time asymptotics and preservation of a generalized concavity of the solutions. We also recover the equality condition in the special case of the Pr\'ekopa--Leindler inequality by further exploiting known properties of the heat equation including the eventual log-concavity and backward uniqueness of solutions.

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Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy

2024-06-17

Qing Liu , Erbol Zhanpeisov

We study a general class of fully nonlinear boundary-degenerate elliptic equations that admit a trivial solution. Although no boundary conditions are posed together with the equations, we show that the … We study a general class of fully nonlinear boundary-degenerate elliptic equations that admit a trivial solution. Although no boundary conditions are posed together with the equations, we show that the operator degeneracy actually generates an implicit boundary condition. Under appropriate assumptions on the degeneracy rate and regularity of the operator, we then prove that there exist no bounded solutions other than the trivial one. Our method is based on the arguments for uniqueness of viscosity solutions to state constraint problems for Hamilton-Jacobi equations. We obtain similar results for fully nonlinear degenerate parabolic equations. Several concrete examples of the equations that satisfy the assumptions are also given.

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A Representation Formula for Viscosity Solutions of Nonlocal Hamilton–Jacobi Equations and Applications

2024-09-03

Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

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Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy

2025-02-05

Qing Liu , Erbol Zhanpeisov

Monge solutions of time-dependent Hamilton-Jacobi equations in metric spaces

2025-02-07

Qing Liu , Made Benny Prasetya Wiranata

As a classical notion equivalent to viscosity solutions, Monge solutions are well understood for stationary Hamilton-Jacobi equations in Euclidean spaces and have been recently studied in general metric spaces. In … As a classical notion equivalent to viscosity solutions, Monge solutions are well understood for stationary Hamilton-Jacobi equations in Euclidean spaces and have been recently studied in general metric spaces. In this paper, we introduce a notion of Monge solutions for time-dependent Hamilton-Jacobi equations in metric spaces. The key idea is to reformulate the equation as a stationary problem under the assumption of Lipschitz regularity for the initial data. We establish the uniqueness and existence of bounded Lipschitz Monge solutions to the initial value problem and discuss their equivalence with existing notions of metric viscosity solutions.

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Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations

2025-03-12

Federica Dragoni , Qing Liu , Zhang Ye

Abstract We show that the square of Carnot–Carathéodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We … Abstract We show that the square of Carnot–Carathéodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We first give a proof in the case of ideal Carnot groups, based on the simple group structure as well as estimates for the Euclidean semiconcavity. Our proof of the general result involves more geometric properties of step 2 Carnot groups. We further apply our h-semiconcavity result to show h-semiconcavity of the viscosity solutions to a class of non-coercive evolutive Hamilton–Jacobi equations by using the Hopf–Lax formula associated to the Carnot–Carathéodory metric.

A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow

2025-01-01

Antoni Kijowski , Qing Liu , Ye Zhang +1 more

Large-time Asymptotics for One-dimensional DirichletProblems for Hamilton-Jacobi Equations withNoncoercive Hamiltonians

2011-01-20

Yoshikazu Giga , Qing Liu , Mitake Hiroyoshi

Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations

2025-03-12

Federica Dragoni , Qing Liu , Zhang Ye

Monge solutions of time-dependent Hamilton-Jacobi equations in metric spaces

2025-02-07

Qing Liu , Made Benny Prasetya Wiranata

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Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy

2025-02-05

Qing Liu , Erbol Zhanpeisov

A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow

2025-01-01

Antoni Kijowski , Qing Liu , Ye Zhang +1 more

A Representation Formula for Viscosity Solutions of Nonlocal Hamilton–Jacobi Equations and Applications

2024-09-03

Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

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Discontinuous eikonal equations in metric measure spaces

2024-08-07

Qing Liu , Nageswari Shanmugalingam , Xiaodan Zhou

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Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy

2024-06-17

Qing Liu , Erbol Zhanpeisov

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A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality

2024-05-26

Kazuhiro Ishige , Qing Liu , Paolo Salani

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Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations

2022-12-12

Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

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A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications

2021-03-24

Nao Hamamuki , Qing Liu

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Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations

2021-02-10

Qing Liu , Xiaodan Zhou

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Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games

2021-01-01

Qing Liu

Singular Neumann Boundary Problems for a Class of Fully Nonlinear Parabolic Equations in One Dimension

2021-01-01

Takashi Kagaya , Qing Liu

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Equivalence of solutions of eikonal equation in metric spaces

2020-10-21

Qing Liu , Nageswari Shanmugalingam , Xiaodan Zhou

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The vanishing exponent limit for motion by a power of mean curvature

2020-04-15

Qing Liu

A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions

2019-12-09

Nao Hamamuki , Qing Liu

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Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations

2019-12-09

Kazuhiro Ishige , Qing Liu , Paolo Salani

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On a discrete scheme for time fractional fully nonlinear evolution equations

2019-11-01

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

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Waiting time effect for motion by positive second derivatives and applications

2013-12-30

Qing Liu

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THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS

2013-12-13

Qing Liu , Tiantian Mao , Taizhong Hu

On the characterization of $p$-harmonic functions on the Heisenberg group by mean value properties

2013-12-10

Fausto Ferrari , Qing Liu , Juan J. Manfredi

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Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations

2013-09-04

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

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On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group

2013-06-10

Fausto Ferrari , Qing Liu , Juan J. Manfredi

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Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton–Jacobi equations with noncoercive Hamiltonians

2011-11-08

Yoshikazu Giga , Qing Liu , Hiroyoshi Mitake

Coauthor	Papers Together
Xiaodan Zhou	9
Hiroyoshi Mitake	7
Yoshikazu Giga	6
Takashi Kagaya	4
Nageswari Shanmugalingam	3
Juan J. Manfredi	3
Erbol Zhanpeisov	2
Paolo Salani	2
Nao Hamamuki	2
Fausto Ferrari	2
Kazuhiro Ishige	2
Robin Ming Chen	2
Armin Schikorra	2
Atsushi Nakayasu	1
Zhang Ye	1
Made Benny Prasetya Wiranata	1
Ellen Shiting Bao	1
Taizhong Hu	1
Stéphane Bressan	1
Tie Luo	1
Federica Dragoni	1
Ruiming Tang	1
Tiantian Mao	1
Antoni Kijowski	1
Ye Zhang	1
Naoki Yamada	1
Mitake Hiroyoshi	1