Regularity theory for fully nonlinear integro-differential equations

2007/09/30 by Luis Caffarelli, Luis Silvestre · 2 citations
Mathematics · #math.AP

paper · pdf · doi:10.1002/cpa.20274

Minor typos corrected, and some extra comments added

arxiv created 2008/04/26 · arxiv updated 2010/03/31

Abstract

We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump Lèvy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior C^1,α regularity for general fully nonlinear integro-differential equations. Our estimates remain uniform as the degree of the equation approaches two, so they can be seen as a natural extension of the regularity theory for elliptic partial differential equations.

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