Monotonicity of solutions for the uniformly elliptic nonlocal Bellman equation on the upper half space

DOI10.1016/j.jmaa.2020.124843zbMath1459.35151OpenAlexW3110838736MaRDI QIDQ1997237

Xueying Chen, Guanfeng Li, Gejun Bao

Publication date: 1 March 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2020.124843

zbMATH Keywords

sliding methodmonotinicity and uniqueness of solutionsuniformly elliptic nonlocal Bellman operator

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Dirichlet series, exponential series and other series in one complex variable (30B50) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• A direct method of moving planes for the fractional Laplacian
• Monotonicity and symmetry of solutions to fractional Laplacian equation
• Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control
• Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
• Symmetry and related properties via the maximum principle
• A priori estimates for prescribing scalar curvature equations
• Direct method of moving planes for logarithmic Laplacian system in bounded domains
• 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
• Fractional equations with indefinite nonlinearities
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• The sliding method for the nonlocal Monge-Ampère operator
• The sliding methods for the fractional \(p\)-Laplacian
• Symmetry of positive solutions for Choquard equations with fractional \(p\)-Laplacian
• Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• The Fractional Laplacian
• On the method of moving planes and the sliding method