Vol. 10, No. 5, 2017

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Perron's method for nonlocal fully nonlinear equations

Chenchen Mou

Vol. 10 (2017), No. 5, 1227–1254
Abstract

This paper is concerned with the existence of viscosity solutions of nonlocal fully nonlinear equations that are not translation-invariant. We construct a discontinuous viscosity solution of such a nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.

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Keywords
viscosity solution, integro-PDE, Hamilton–Jacobi–Bellman–Isaacs equation, Perron's method, weak Harnack inequality
Mathematical Subject Classification 2010
Primary: 35D40, 35J60, 35R09, 47G20, 49N70
Secondary: 45K05
Milestones
Received: 24 November 2016
Revised: 1 February 2017
Accepted: 24 April 2017
Published: 1 July 2017
Authors
Chenchen Mou
Department of Mathematics
UCLA
Los Angeles, CA 90095
United States