Regularity for anisotropic fully nonlinear integro-differential equations

Luis A. Caffarelli, Raimundo Leitão, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish (US)
Pages (from-to)681-714
Number of pages34
JournalMathematische Annalen
Issue number3-4
StatePublished - Dec 1 2014
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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