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arXiv · 2105.09417

Nonlocal fully nonlinear double obstacle problems

Mohammad Safdari
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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.

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Mohammad Safdari. 2021-05-19. Nonlocal fully nonlinear double obstacle problems. https://arxiv.org/abs/2105.09417

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