SU\G(𝔾)/K·U
Mathematics â€ș Applied Mathematics

Nonlinear Partial Differential Equations

Works Count: 42231

Description

This cluster of papers focuses on the theory of fractional Laplacian operators, including topics such as Sobolev spaces, nonlinear equations, regularity theory, variational problems, critical exponents, ground state solutions, elliptic equations, nonlocal operators, and Hamiltonian estimates.

Keywords

Fractional Laplacian; Sobolev Spaces; Nonlinear Equations; Regularity Theory; Variational Problems; Critical Exponents; Ground State Solutions; Elliptic Equations; Nonlocal Operators; Hamiltonian Estimates

Most Cited Works

Action Title Date Authors
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A Lower Bound for the Smallest Eigenvalue of the Laplacian 2015-04-11 Jeff Cheeger
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Nonlinear Analysis on Manifolds. Monge-AmpĂšre Equations 1982-01-01 Thierry Aubin
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The heat equation shrinks embedded plane curves to round points 1987-01-01 M. Grayson
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Fully Nonlinear Elliptic Equations 1995-09-22 Luis Caffarelli Xavier Cabré
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Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds 1982-01-01 Jeff Cheeger M. Gromov Michael E. Taylor
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Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities 2000-10-27 Emmanuel Hebey
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The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. 1984-04-01 Pierre‐Louis Lions
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Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation 1977-10-01 Élliott H. Lieb
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ProblÚmes isopérimétriques et espaces de Sobolev 1976-01-01 Thierry Aubin
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Classification of solutions of some nonlinear elliptic equations 1991-08-01 Wenxiong Chen Congming Li
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On the parabolic kernel of the Schrödinger operator 1986-01-01 Peter Li Shing Tung Yau
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The local regularity of solutions of degenerate elliptic equations 1982-01-01 Eugene B. Fabes Carlos E. Kenig Raul Serapioni
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Uniqueness of positive solutions of Δu−u+up=0 in Rn 1989-09-01 Man Kam Kwong
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Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities 2002-01-01 Élliott H. Lieb
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Regularity for a more general class of quasilinear elliptic equations 1984-01-01 Peter Tolksdorf
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Dual variational methods in critical point theory and applications 1973-12-01 Antonio Ambrosetti Paul H. Rabinowitz
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Symmetry and related properties via the maximum principle 1979-10-01 Basilis Gidas Wei‐Ming Ni Louis Nirenberg
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The Yamabe problem 1987-01-01 John M. Lee Thomas H. Parker
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Boundary regularity for solutions of degenerate elliptic equations 1988-11-01 Gary M. Lieberman
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Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems 1994-06-01 Antonio Ambrosetti Haïm Brézis G. Cerami
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Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system 1986-04-01 Yoshikazu Giga
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Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation 2010-04-25 Luis Caffarelli Alexis Vasseur
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HitchhikerÊŒs guide to the fractional Sobolev spaces 2011-12-30 Eleonora Di Nezza Giampiero Palatucci Enrico Valdinoci
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Best constant in Sobolev inequality 1976-12-01 Giorgio Talenti
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Partial regularity of suitable weak solutions of the navier‐stokes equations 1982-11-01 Luis Caffarelli Robert V. Kohn Louis Nirenberg
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Non-linear elliptic and parabolic equations involving measure data 1989-11-01 Lucio Boccardo Thierry Gallouët
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C1 + α local regularity of weak solutions of degenerate elliptic equations 1983-01-01 Emmanuele DiBenedetto
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On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω) 2001-11-01 Xianling Fan Dun Zhao
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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents 1983-07-01 Haïm Brézis Louis Nirenberg
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THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION 2001-01-31 FĂ©lix Otto
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Minimax Methods in Critical Point Theory with Applications to Differential Equations 1986-07-01 P. Rabinowitz
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A relation between pointwise convergence of functions and convergence of functionals 1983-07-01 HaĂŻm BrĂ©zis Élliott H. Lieb
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Global and local behavior of positive solutions of nonlinear elliptic equations 1981-07-01 Basilis Gidas Joel Spruck
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A Strong Maximum Principle for some quasilinear elliptic equations 1984-10-01 Juan-Luis Vïżœzquez
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Motion of level sets by mean curvature. I 1991-01-01 L. C. Evans Joel Spruck
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Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth 1989-04-01 Luis Caffarelli Basilis Gidas Joel Spruck
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Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality 2000-06-01 FĂ©lix Otto CĂ©dric Villani
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Regularity of the obstacle problem for a fractional power of the laplace operator 2006-08-09 LuĂ­s Silvestre
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Polar factorization and monotone rearrangement of vector‐valued functions 1991-06-01 Yann Brenier
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Nonconvex minimization problems 1979-01-01 Ivar Ekeland
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Conformal deformation of a Riemannian metric to constant scalar curvature 1984-01-01 Richard Schoen
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Logarithmic Sobolev Inequalities 1975-01-01 Leonard Gross
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On a class of nonlinear Schrïżœdinger equations 1992-03-01 Paul H. Rabinowitz
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The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 1984-08-01 Pierre‐Louis Lions
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Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations 1991-01-01 Yun Gang Chen Yoshikazu Giga Shun’ichi Goto
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An Extension Problem Related to the Fractional Laplacian 2007-08-08 Luis Caffarelli LuĂ­s Silvestre
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Progress in Nonlinear Differential Equations and their Applications 2006-01-01 Amandine Aftalion
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Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities 1983-09-01 Élliott H. Lieb
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II 1964-02-01 Shmuel Agmon Avron Douglis Louis Nirenberg
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Le problĂšme de Dirichlet pour les Ă©quations elliptiques du second ordre Ă  coefficients discontinus 1965-01-01 Laure Cardoulis Michel Cristofol

Most Recent Works

Action Title Date Authors
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A clustering theorem in fractional Sobolev spaces 2025-04-29 Fatma Gamze DĂŒzgĂŒn Antonio Iannizzotto Vincenzo Vespri
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Campanato Type Estimates for the Multi-phase Problems with Irregular Obstacles 2025-04-29 Bin Ge Beilei Zhang
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Prescribing positive curvature with conical singularities on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">S</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> 2025-04-29 Jingyi Chen Yuxiang Li Yunqing Wu
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Boundary regularity of unbounded weak solutions of the oblique derivative problem for a class of strongly nonlinear elliptic systems 2025-04-29 A. A. Arkhipova
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On Sharp Anisotropic Hardy Inequalities 2025-04-30 Xia Huang Dong Ye
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Existence of the fully nontrivial ground state solutions for the coupled nonlinear Brezis-Nirenberg Maxwell system 2025-04-30 Li Cong Yong Liu Jun Wang Yang Wen
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Boundary Concentrated Solutions for an Elliptic Equation with Subcritical Nonlinearity 2025-04-30 Saleh Hadi Alharbi Mohamed Ben Ayed
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Multiple Solutions of Fractional Kazdan–Warner Equation for Negative Case on Finite Graphs 2025-04-30 Liang Shan Yang Liu
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On a nonlinear partial differential equation with a $$p\left( .\right) $$-triharmonic operator 2025-04-30 İsmail Aydın Khaled Kefi
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No formation of a new phase for a free boundary problem in combustion theory 2025-04-30 Ken Furukawa Yoshikazu Giga Naoto Kajiwara
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Boundary Blowing Up Solutions for an Elliptic Neumann Problem with Nearly Critical Exponent 2025-05-01 Rakan Almushahhin Mohamed Ben Ayed
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Existence of weak solutions to degenerate Leray–Lions operators in weighted quasilinear elliptic equations with variable exponents, indefinite nonlinearity, and Hardy-type term 2025-05-01 Khaled Kefi
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Self-similar solutions of fast reaction limit problem with nonlinear diffusion 2025-05-01 Elaine Crooks Yini Du
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Infinitely many solutions for a class of fractional equations via variant fountain theorems 2025-04-30 Abdelilah Azghay Mohammed Massar Abderrahim El Mhouti
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Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces 2025-05-02 Joohak Bae Jae-Hoon Kang Panki Kim Jaehun Lee
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Restriction Estimates for Hyperbolic Paraboloids in Higher Dimensions 2025-05-02 Zhuoran Li
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Inverse coefficient problems for the heat equation with fractional Laplacian 2025-05-02 Azizbek Mamanazarov Durvudkhan Suragan
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On the influence of some absorption terms on the solutions of nonlinear parabolic equations 2025-05-02 Maria Michaela Porzio
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Local boundedness and higher integrability for the sub-critical singular porous medium system 2025-05-02 Verena Bögelein Frank Duzaar Ugo Gianazza Naian Liao
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Existence of Normalized Solutions of a Hartree–Fock System With Mass Subcritical Growth 2025-05-02 Hua Jin Y. Austin Chang Marco Squassina Jianjun Zhang
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Characterization and Behavior of Multi-Peak Solutions for the Schrödinger-Poisson System 2025-05-03 Qingjie Guo Shixin Wen Jianghua Ye
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Euler equations in Sobolev conormal spaces 2025-05-03 Mustafa Sencer Aydın Igor Kukavica
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Existence and multiplicity of solutions for subquadratic fractional Hamiltonian systems 2025-05-03 Mohsen Timoumi
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Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces 2025-05-04 Wojciech GĂłrny
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A game interpretation for the weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg" display="inline" id="d1e41"><mml:mi>p</mml:mi></mml:math>-Laplace equation 2025-05-05 Mamoru Aihara
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Optimal metrics for the first curl eigenvalue on 3-manifolds 2025-05-05 Alberto Enciso Wadim Gerner Daniel Peralta‐Salas
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Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations 2025-05-05 Yohei Fujishima Toru Kan
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Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian 2025-05-05 José Carmona Rubén Fiñana Arånega
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The existence of solutions for Schrödinger-Poisson equation with zero mass and a convolution nonlinearity 2025-05-01 Xianhua Tang Jiuyang Wei
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Asymptotic boundary behavior of large solutions to equations involving infinity Laplacian 2025-05-05 Ling Mi Yuan Yue
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Existence and asymptotical behavior of solutions for a fractional logarithmic Schrödinger-Poisson system 2025-05-05 Jiaqi Dou Qi Gao Zhengping Wang
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Gradient estimates for nonlinear equations with measurable nonlinearities from composite material 2025-05-05 Yunsoo Jang
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Entire solutions to the Swift–Hohenberg equation via a variational approach 2025-05-05 Sergey B. Kolonitskii L. M. Lerman Alexander I. Nazarov
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Semiclassical solutions for critical Schrödinger–Poisson systems involving multiple competing potentials 2025-05-04 Lingzheng Kong Haibo Chen
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The molecular characterizations of variable Triebel-Lizorkin spaces associated with the Hermite operator and its applications 2025-05-01 Qi Sun Ciqiang Zhuo
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On the first eigenvalue of the (p, q)-Laplacian and some related problems 2025-05-06 Said El Manouni Kanishka Perera Patrick Winkert
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L maximal bounds and Sobolev regularity of two-parameter averages over tori 2025-05-06 Ju Young Lee Sanghyuk Lee
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Weak solutions in anisotropic (α→(z),ÎČ→(z))-Laplacian Kirchhoff models 2025-05-05 Ahmed Ahmed Mohamed Saad Bouh Elemine Vall
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$$C^\infty $$ regularity in semilinear free boundary problems 2025-05-07 Daniel Herrera Restrepo Xavier Ros‐Oton
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Multiplicity results for mass constrained Allen–Cahn equations on Riemannian manifolds with boundary 2025-05-07 Dario Corona Stefano Nardulli Ramon Oliver-Bonafoux Giandomenico Orlandi P. Piccione
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On the sharp second order Caffarelli–Kohn–Nirenberg inequality 2025-05-06 Anh Tuan Duong Van Hoang Nguyen
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Lusin approximation for functions of bounded variation 2025-05-08 Panu Lahti Khanh Ngoc Nguyen
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A weighted weak-type multilinear gradient inequality 2025-05-07 VĂ­ctor GarcĂ­a GarcĂ­a Pedro Ortega Salvador
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Weighted Gagliardo–Nirenberg Inequalities via Optimal Transport Theory and Applications 2025-05-07 Zoltán M. Balogh Sebastiano Don Alexandru Kristály
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THE MINTY-BROWDER THEORY FOR P(X)-LAPLACIAN EQUATIONS WITH PSEUDO-MONOTONE OPERATOR 2025-05-01 Mykola Yaremenko
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EXISTENCE OF SOLUTIONS FOR THE FRACTIONAL KIRCHHOFF PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY 2025-05-07 Ihya Talibi Brahim El Boukari Jalila El Ghordaf
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Weighted Variational Inequalities for Heat Semigroups Associated with Schrödinger Operators Related to Critical Radius Functions 2025-05-08 Yongming Wen Huoxiong Wu
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On the embedding of weighted Sobolev spaces with applications to a planar nonlinear Schrödinger equation 2025-05-01 Antonio Azzollini Alessio Pomponio Simone Secchi
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On higher integrability of minimizer to a nonlinear functional in domains perforated along the boundary 2025-05-09 Г. А. ЧДчĐșĐžĐœ
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Dirichlet problems for elliptic Waldenfels operators and Feller semigroups 2025-05-11 Kazuaki Taira