On a fractional Monge-Ampère operator

DOI10.1007/S40818-015-0005-XzbMath1393.35268arXiv1402.6370OpenAlexW3102241819MaRDI QIDQ1661376

Fernando Charro, Luis A. Caffarelli

Publication date: 16 August 2018

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6370

zbMATH Keywords

integro-differential equationsnonlinear elliptic equationsMonge-Ampère

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Fractional partial differential equations (35R11) Monge-Ampère equations (35J96)

Related Items (14)

Symmetry of solutions for a class of nonlocal Monge–Ampère equations ⋮ A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity ⋮ Fractional convexity ⋮ Monotonicity of solutions for a class of nonlocal Monge-Ampère problem ⋮ Harnack inequality for the fractional nonlocal linearized Monge-Ampère equation ⋮ 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 ⋮ On a family of fully nonlinear integrodifferential operators: from fractional Laplacian to nonlocal Monge-Ampère ⋮ The obstacle problem for a fractional Monge–Ampère equation ⋮ Min-max formulas for nonlocal elliptic operators on Euclidean space ⋮ The sliding method for the nonlocal Monge-Ampère operator ⋮ Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality ⋮ Monotonicity of solutions for the uniformly elliptic nonlocal Bellman equation on the upper half space

Cites Work

• Unnamed Item
• A non-local Monge-Ampère equation
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations
• Existence of entire solutions to the Monge-Ampère equation
• Regularity theory for fully nonlinear integro-differential equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The Monge-Ampère equation

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