Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications

DOI10.1007/s10231-020-01027-9zbMath1467.35072arXiv2004.02879OpenAlexW3048689109MaRDI QIDQ2663151

Wei Dai, Guolin Qin

Publication date: 16 April 2021

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02879

zbMATH Keywords

monotonicityasymptotic propertiessymmetry and uniquenessuniformly elliptic nonlocal Monge-Ampère operator

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Monge-Ampère equations (35J96) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (6)

Monotonicity of solutions for a class of uniformly elliptic nonlocal Bellman systems ⋮ Maximum principles and qualitative properties of solutions for nonlocal double phase operator ⋮ Monotonicity of solutions for parabolic equations involving nonlocal Monge-Ampère operator ⋮ Asymptotic symmetry and monotonicity of solutions for weighted fractional parabolic equations ⋮ Radial symmetry and monotonicity of the positive solutions for \(k\)-Hessian equations ⋮ Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A non-local Monge-Ampère equation
• Boundary regularity for fully nonlinear integro-differential equations
• A direct method of moving planes for the fractional Laplacian
• Monotonicity and symmetry of solutions to fractional Laplacian equation
• Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
• Fractional Laplacian in conformal geometry
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• \(C^ 2\) a priori estimates for degenerate Monge-Ampère 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
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Existence and non-existence of solutions for a class of Monge-Ampère equations
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• Classification of solutions of higher order conformally invariant equations
• On uniqueness of solutions of \(n\)-th order differential equations in conformal geometry
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• On the Dirichlet problem for degenerate Monge-Ampère equations.
• 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
• Classification of nonnegative classical solutions to third-order equations
• Direct methods on fractional equations
• Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes
• Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• The sliding method for the nonlocal Monge-Ampère operator
• Direct methods for pseudo-relativistic Schrödinger operators
• Liouville theorem for poly-harmonic functions on \(\mathbb{R}^n_+ \)
• The sliding methods for the fractional \(p\)-Laplacian
• Principal eigenvalues of a class of nonlinear integro-differential operators
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• A symmetry problem in potential theory
• Entire $s$-harmonic functions are affine
• Uniqueness of Radial Solutions for the Fractional Laplacian
• A concave—convex elliptic problem involving the fractional Laplacian
• Existence of entire solutions to the Monge-Ampère equation
• Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Euler Equations, Navier-Stokes Equations and Turbulence
• Regularity theory for fully nonlinear integro-differential equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Monotonicity and Symmetry of Solutions of Fully Nonlinear Elliptic Equations on Bounded domains
• Existence and non-existence results for semilinear elliptic problems in unbounded domains
• Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity
• A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space
• The Fractional Laplacian
• On the method of moving planes and the sliding method
• The maximum principles for fractional Laplacian equations and their applications
• A note on the monotonicity of solutions for fractional equations in half-spaces
• RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN
• An Extension Problem Related to the Fractional Laplacian
• Classification of solutions for an integral equation

This page was built for publication: Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications