Regularity for anisotropic fully nonlinear integro-differential equations

Jos\'e Miguel Urbano; Luis A. Caffarelli; Raimundo Leit\~ao

arxiv: 1311.0795 · v1 · pith:DI7OHQFTnew · submitted 2013-11-04 · 🧮 math.AP

Regularity for anisotropic fully nonlinear integro-differential equations

Luis A. Caffarelli , Raimundo Leit\~ao , Jos\'e Miguel Urbano This is my paper

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keywords anisotropicdifferentequationsfullyintegro-differentialnonlinearregularitycaffarelli

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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 $C^{1, \gamma}$ regularity, extending the results of [Caffarelli and Silvestre, CPAM 62, 2009] to the anisotropic case.

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Regularity for anisotropic fully nonlinear integro-differential equations

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