The sliding methods for the fractional \(p\)-Laplacian

DOI10.1016/j.aim.2019.106933OpenAlexW2993817511WikidataQ126625825 ScholiaQ126625825MaRDI QIDQ2288080

Leyun Wu, Wenxiong Chen

Publication date: 17 January 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2019.106933

zbMATH Keywords

fractional \(p\)-Laplaciannarrow region principlemonotonicity of solutionssliding methods

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Liouville-type results for positive solutions of pseudo-relativistic Schrödinger system ⋮ Qualitative properties of singular solutions to fractional elliptic equations ⋮ Sliding method for fully nonlinear fractional order equations ⋮ Monotonicity of solutions for a class of nonlocal Monge-Ampère problem ⋮ Sub-solutions and a point-wise Hopf's lemma for fractional \(p\)-Laplacian ⋮ Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications ⋮ Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system ⋮ Monotonicity and uniqueness of positive solutions to elliptic fractional \(p\)-equations ⋮ Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations ⋮ Monotonicity of positive solutions for fractional \(p\)-systems in unbounded Lipschitz domains ⋮ Monotonicity of solutions for nonlocal double phase equations in bounded domains and the whole space ⋮ Monotonicity of solutions for weighted fractional parabolic equations on the upper half space ⋮ Asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space ⋮ Maximum principles and qualitative properties of solutions for nonlocal double phase operator ⋮ Monotonicity of standing waves for the generalized fractional Schrödinger equations ⋮ Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case ⋮ Nonexistence of solutions for tempered fractional parabolic equations ⋮ The radial symmetry of positive solutions for semilinear problems involving weighted fractional Laplacians ⋮ Classification of solutions to several semi-linear polyharmonic equations and fractional equations ⋮ Maximum principles involving the uniformly elliptic nonlocal operator ⋮ Monotonicity and one-dimensional symmetry of solutions for fractional reaction-diffusion equations and various applications of sliding methods ⋮ Asymptotic symmetry and monotonicity of solutions for weighted fractional parabolic equations ⋮ Monotonicity results for fractional parabolic equations in the whole space ⋮ Monotonicity of solutions for the system with pseudo-relativistic Schrödinger operators ⋮ Asymptotic method of moving planes for fractional parabolic equations ⋮ Maximum principles, Liouville theorem and symmetry results for the fractional \(g\)-Laplacian ⋮ Monotonicity of positive solutions for nonlocal problems in unbounded domains ⋮ Nonexistence of solutions for indefinite fractional parabolic equations ⋮ Liouville theorems for fractional parabolic equations ⋮ The sliding method for the nonlocal Monge-Ampère operator ⋮ Monotonicity results for the fractional p-Laplacian in unbounded domains ⋮ Monotonicity of solutions for the uniformly elliptic nonlocal Bellman equation on the upper half space ⋮ Sliding method for the semi-linear elliptic equations involving the uniformly elliptic nonlocal operators ⋮ Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations ⋮ Liouville theorem involving the uniformly nonlocal operator ⋮ Sliding methods for the higher order fractional Laplacians ⋮ Direct methods for pseudo-relativistic Schrödinger operators ⋮ A direct method of moving planes for fully nonlinear nonlocal operators and applications ⋮ Nonexistence of positive solutions for an indefinite fractional \(p\)-Laplacian equation ⋮ Sliding methods for a class of generalized fractional Laplacian equations ⋮ Existence of solutions to fractional \(p\)-Laplacian systems with homogeneous nonlinearities of critical Sobolev growth ⋮ Monotonicity of solutions for fractional \(p\)-equations with a gradient term ⋮ Hopf's lemmas for parabolic fractional \(p\)-Laplacians ⋮ Nehari manifold for weighted singular fractional \(p\)-Laplace equations ⋮ Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman system ⋮ The sliding method for fractional Laplacian systems ⋮ Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
• Non-local gradient dependent operators
• Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian
• A direct method of moving planes for the fractional Laplacian
• Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
• Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
• A nonlocal anisotropic model for phase transitions
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• Maximum principles for the fractional p-Laplacian and symmetry of solutions
• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• Symmetry and nonexistence of positive solutions to fractional \(p\)-Laplacian equations
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
• Liouville theorems involving the fractional Laplacian on a half space
• A class of integral equations and approximation of \(p\)-Laplace equations
• Indefinite fractional elliptic problem and Liouville theorems
• A concave—convex elliptic problem involving the fractional Laplacian
• From the long jump random walk to the fractional Laplacian
• Nonlocal Tug-of-War and the Infinity Fractional Laplacian
• A Hopf type lemma for fractional equations
• The Fractional Laplacian
• On the method of moving planes and the sliding method
• Classification of solutions for an integral equation