Regularity for anisotropic fully nonlinear integro-differential equations

2013/11/04 by Caffarelli, Luis A., Leitão, Raimundo, Urbano, José Miguel · 1 citation
#35B65 #35D40 #35J60 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1311.0795

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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• Some remarks on Campanato Theorem and the Anisotropic Bessel Spaces

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