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arXiv · 0709.4681

Regularity theory for fully nonlinear integro-differential equations

Luis Caffarelli·Luis Silvestre
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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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Luis Caffarelli, Luis Silvestre. 2008-04-26. Regularity theory for fully nonlinear integro-differential equations. https://doi.org/10.1002/cpa.20274

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