Perron’s method for nonlocal fully nonlinear equations

Mou, Chenchen

doi:10.2140/apde.2017.10.1227

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Perron's method for nonlocal fully nonlinear equations

Chenchen Mou

Vol. 10 (2017), No. 5, 1227–1254

DOI: 10.2140/apde.2017.10.1227

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.

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

Vol. 10, No. 5, 2017