The sliding method for the nonlocal Monge-Ampère operator

DOI10.1016/j.na.2020.111786zbMath1437.35419OpenAlexW3006089268MaRDI QIDQ1988406

Gejun Bao, Xueying Chen, Guanfeng Li

Publication date: 23 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.111786

zbMATH Keywords

sliding methodnarrow region principlemonotonicity of solutionsnonlocal Monge-Ampère operator

Mathematics Subject Classification ID

Monge-Ampère equations (35J96)

Related Items

Sliding method for fully nonlinear fractional order equations, Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications, Monotonicity of solutions for a class of uniformly elliptic nonlocal Bellman systems, Monotonicity of solutions for parabolic equations involving nonlocal Monge-Ampère operator, Maximum principles involving the uniformly elliptic nonlocal operator, 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, Sliding methods for a class of generalized fractional Laplacian equations, The sliding method for fractional Laplacian systems

Cites Work

• Unnamed Item
• Unnamed Item
• A direct method of moving planes for the fractional Laplacian
• Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
• Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
• Moving planes for nonlinear fractional Laplacian equation with negative powers
• On a fractional Monge-Ampère operator
• 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
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• The sliding methods for the fractional \(p\)-Laplacian
• Liouville theorems involving the fractional Laplacian on a half space
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Sharp energy estimates for nonlinear fractional diffusion equations
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• On Fractional Laplacians
• On the method of moving planes and the sliding method
• RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN
• An Extension Problem Related to the Fractional Laplacian
• Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions