Nonlocal fully nonlinear double obstacle problems

Abstract

We prove the existence and $C^{1,\alpha }$ regularity of solutions to nonlocal fully nonlinear elliptic double obstacle problems. We also obtain boundary regularity for these problems. The obstacles are assumed to be Lipschitz semi-concave/semi-convex functions, and we do not require them to be $C^1$. Our approach is to adapt a penalization method to be applicable to the setting of nonlocal equations and their viscosity solutions.

arXiv comment15 pages

References in corpus (4)

• Regularity theory for fully nonlinear integro-differential equations
• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
• Obstacle problems for integro-differential operators: Regularity of solutions and free boundaries
• Double Obstacle Problems with obstacles given by non-$C^2$ Hamilton-Jacobi equations

Cited by in corpus (1)

• Nonlocal equations with gradient constraints