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arXiv:1809.06821 [math.AP]AbstractReferencesReviewsResources

Fully nonlinear integro-differential equations with deforming kernels

Luis Caffarelli, Rafayel Teymurazyan, José Miguel Urbano

Published 2018-09-18Version 1

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.

Comments: 25 pages
Categories: math.AP
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