The obstacle problem for a fractional Monge--Ampère equation

2017/12/19 by Yash Jhaveri, Y. Jhaveri, Jhaveri, Y. +3
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.CA

paper · pdf · doi:10.48550/arxiv.1712.07226

23 pages. To appear in Communications in Partial Differential Equations

openalex publication_date 2017/12/19 · arxiv created 2019/11/19 · arxiv updated 2019/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the obstacle problem for a nonlocal, degenerate elliptic Monge--Ampère equation. We show existence and regularity of a unique classical solution to the problem and regularity of the free boundary.

Citations

• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

Related

• Regularity of free boundary for the Monge-Ampère obstacle problem
• The obstacle problem for nonlinear integro-differential operators
• An obstacle problem for a class of Monge-Ampère type functionals
• On the singular set of the free boundary for a Monge-Ampère obstacle problem
• C^1,α regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator