Fully nonlinear integro-differential equations with deforming kernels (1809.06821v2)

Published 18 Sep 2018 in math.AP

Abstract: We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Amp`{e}re equation. We prove an ABP estimate and a Harnack inequality and derive H\"{o}lder and $C^{1,\alpha}$ regularity results for solutions.

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