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 SS, we prove the discontinuous viscosity solution is H\"older continuous and thus it is a viscosity solution.
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