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arXiv · 1311.0795

Regularity for anisotropic fully nonlinear integro-differential equations

Luis A. Caffarelli·Raimundo Leitão·José Miguel Urbano
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Abstract

We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior $C^{1, γ}$ regularity, extending the results of [Caffarelli and Silvestre, CPAM 62, 2009] to the anisotropic case.

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Luis A. Caffarelli, Raimundo Leitão, José Miguel Urbano. 2013-11-04. Regularity for anisotropic fully nonlinear integro-differential equations. https://arxiv.org/abs/1311.0795

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