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 (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.
|Original language||English (US)|
|Number of pages||34|
|State||Published - Dec 1 2014|
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