Perron's method for nonlocal fully nonlinear equations

Abstract

This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron's method. If the equation is uniformly elliptic in the sense of \cite{SS}, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.

Added a figure, fixed typos, to appear in Anal. PDE

References in corpus (3)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Regularity for parabolic integro-differential equations with very irregular kernels
• Schauder estimates for solutions of linear parabolic integro-differential equations

Cited by in corpus (2)

• Mixed fully nonlinear local and nonlocal elliptic operators in Heisenberg group
• Nonlocal equations with gradient constraints