Weak KAM aspects of convex Hamilton–Jacobi equations with Neumann type boundary conditions

Hitoshi Ishii

Type: Article

Publication Date: 2010-10-17

Citations: 20

DOI: https://doi.org/10.1016/j.matpur.2010.10.006

View

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Journal de Mathématiques Pures et Appliquées - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Metric formulae for nonconvex Hamilton--Jacobi equations and applications	2011	Antonio Marigonda Antonio Siconolfi
+	Effective nonlinear Neumann boundary conditions for 1D nonconvex Hamilton–Jacobi equations	2017	Jessica Guerand
+	<i>L</i><sup>∞</sup> variational problems and weak KAM theory	2006	Yifeng Yu
+ PDF Chat	Weak KAM theory for HAMILTON-JACOBI equations depending on unknown functions	2016	Jun Yan Lin Wang Xifeng Su
+	Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations with state-constraint	2023	Son N. T. Tu Jianlu Zhang
+	Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set	2012	Albert Fathi
+	Convex sets with obstacle and gradient constraints	2023	Assis Azevedo Davide Azevedo Lisa Santos
+	Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds	2014	Yuedong Kong Junxiang Xu
+ PDF Chat	The Lax–Oleinik semi-group: a Hamiltonian point of view	2012	Patrick Bernard
+	Metric entropy for Hamilton-Jacobi equation with uniformly directionally convex Hamiltonian	2020	Stefano Bianchini Prerona Dutta Khai T. Nguyen
+	Metric entropy for Hamilton-Jacobi equation with uniformly directionally convex Hamiltonian	2020	Stefano Bianchini Prerona Dutta Khai T. Nguyen
+	Strictly convex Hamilton-Jacobi equations: strong trace of the gradient	2023	Régis Monneau
+	The Lax-Oleinik semi-group: a Hamiltonian point of view	2012	Patrick Bernard
+	The Lax-Oleinik semi-group: a Hamiltonian point of view	2012	Patrick Bernard
+	Global structure of Brezis-Nirenberg type equations on the unit ball(Variational Problems and Related Topics)	1996	喜継壁谷晶二四ツ谷英二柳田
+	Global structure of Brezis-Nirenberg type equations on the unit ball(Variational Problems and Related Topics)	1996	Yoshitsugu Kabeya Shoji Yotsutani Eiji Yanagida
+	Hamilton-Jacobi Equations and Weak KAM Theory	2013	Antonio Siconolfi
+ PDF Chat	The Neumann problem for a class of Hessian quotient type equations	2025	Jianhua Gong Zixuan Liu Qiang Tu
+	Weak KAM theory for general Hamilton-Jacobi equations III: the variational principle under Osgood conditions	2014	Lin Wang Jun Yan
+	Aubry-Mather and weak KAM theories for contact Hamiltonian systems. Part 2: Strictly decreasing case	2018	Kaizhi Wang Lin Wang Jun Yan

Cited by (19)

Action	Title	Year	Authors
+	Weak KAM theory for nonregular commuting Hamiltonians	2012	Andrea Davini Maxime Zavidovique
+ PDF Chat	Singularly perturbed spectral problems with Neumann boundary conditions	2015	Andrey Piatnitski Antonina Rybalko Volodymyr Rybalko
+ PDF Chat	Long-time asymptotic solutions of convex hamilton-jacobi equations depending on unknown functions	2017	Xia Li
+ PDF Chat	Asymptotic analysis for the eikonal equation with the dynamical boundary conditions	2014	Eman Salem Alaidarous Ebraheem Alzahrani Hitoshi Ishii Arshad M. M. Younas
+ PDF Chat	Classifying the level set of principal eigenvalue for time-periodic parabolic operators and applications	2021	Shuang Liu Yuan Lou
+	Weak KAM theoretic aspects for nonregular commuting Hamiltonians	2011	Andrea Davini Maxime Zavidovique
+ PDF Chat	A PDE Approach to Large-Time Asymptotics for Boundary-Value Problems for Nonconvex Hamilton–Jacobi Equations	2011	Guy Barles Hiroyoshi Mitake
+ PDF Chat	Vanishing contact structure problem and convergence of the viscosity solutions	2019	Qinbo Chen Wei Cheng Hitoshi Ishii Kai Zhao
+	The vanishing discount problem and viscosity Mather measures. Part 2: Boundary value problems	2016	Hitoshi Ishii Hiroyoshi Mitake Hung V. Tran
+	Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds	2014	Yuedong Kong Junxiang Xu
+	Singularly perturbed spectral problems with Neumann boundary conditions	2015	Andrey Piatnitski Antonina Rybalko Volodymyr Rybalko
+	A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations	2013	Hitoshi Ishii
+	Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations	2013	Yoshikazu Giga Qing Liu Hiroyoshi Mitake
+	A Characterization of the Reflected Quasipotential	2015	Kasie Geralyn Farlow Martin V. Day
+	Level-set forced mean curvature flow with the Neumann boundary condition	2021	Jiwoong Jang Dohyun Kwon Hiroyoshi Mitake Hung V. Tran
+ PDF Chat	Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions	2010	Hitoshi Ishii
+	A convergence result for the ergodic problem for Hamilton–Jacobi equations with Neumann-type boundary conditions	2016	Eman Salem Alaidarous Ebraheem Alzahrani Hitoshi Ishii Arshad M. M. Younas
+ PDF Chat	On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions	2012	Guy Barles Hiroyoshi Mitake Hitoshi Ishii
+	SINGULAR NEUMANN PROBLEMS AND LARGE-TIME BEHAVIOR OF SOLUTIONS OF NONCOERCIVE HAMILTON-JACOBI EQUATIONS	2010	Yoshikazu Giga Qing Liu Hiroyoshi Mitake

Citing (21)

Action	Title	Year	Authors
+	Aubry-Mather theory and periodic solutions of the forced Burgers equation	1999	E Weinan
+	Fully nonlinear Neumann type boundary conditions for first-order Hamilton–Jacobi equations	1991	Guy Barles Pierre‐Louis Lions
+	Stochastic differential equations with reflecting boundary conditions	1984	Pierre‐Louis Lions Alain‐Sol Sznitman
+	Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians	2008	Naoyuki Ichihara Hitoshi Ishii
+	Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens	1997	Albert Fathi
+	Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation	1986	P. L. Lions Neil S. Trudinger
+ PDF Chat	Asymptotic solutions for large time of Hamilton–Jacobi equations in Euclidean n space	2007	Hitoshi Ishii
+ PDF Chat	Existence of C 1 critical subsolutions of the Hamilton-Jacobi equation	2004	Albert Fathi Antonio Siconolfi
+	A Generalized Dynamical Approach to the Large Time Behavior of Solutions of Hamilton--Jacobi Equations	2006	Andrea Davini Antonio Siconolfi
+	Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians	2007	Hitoshi Ishii Hiroyoshi Mitake
+ PDF Chat	The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations	2008	Hiroyoshi Mitake
+	Semicontinuous Viscosity Solutions For Hamilton–Jacobi Equations With Convex Hamiltonians	1990	E. N. Barron R. Jensen
+	User’s guide to viscosity solutions of second order partial differential equations	1992	Michael G. Crandall Hitoshi Ishii Pierre-Louis Lions
+	A survey of partial differential equations methods in weak KAM theory	2004	Lawrence C. Evans
+	Sur la convergence du semi-groupe de Lax-Oleinik	1998	Albert Fathi
+	Convergence to steady states or periodic solutions in a class of Hamilton–Jacobi equations	2001	Jean‐Michel Roquejoffre
+	Viscosity solutions for partial differential equations with Neumann type boundary conditions and some aspects of Aubry–Mather theory	2007	Oana‐Silvia Serea
+	Fully Non-linear Neumann Type Boundary Conditions for Second-Order Elliptic and Parabolic Equations	1993	Guy Barles
+	PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians	2004	Albert Fathi Antonio Siconolfi
+	Neumann type boundary conditions for Hamilton-Jacobi equations	1985	Pierre‐Louis Lions
+	Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints	2008	Hiroyoshi Mitake