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arXiv · 1809.06821

Fully nonlinear integro-differential equations with deforming kernels

Luis Caffarelli·Rafayel Teymurazyan·José Miguel Urbano
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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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Luis Caffarelli, Rafayel Teymurazyan, José Miguel Urbano. 2018-09-18. Fully nonlinear integro-differential equations with deforming kernels. https://arxiv.org/abs/1809.06821

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