Perron's method for nonlocal fully nonlinear equations

Chenchen Mou

doi:10.2140/apde.2017.10.1227

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Home > Journals > Anal. PDE > Volume 10 > Issue 5 > Article

2017 Perron's method for nonlocal fully nonlinear equations

Chenchen Mou

Anal. PDE 10(5): 1227-1254 (2017). DOI: 10.2140/apde.2017.10.1227

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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.