Regularity theory for fully nonlinear integro-differential equations

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 $C^{1,\alpha }$ 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.

Minor typos corrected, and some extra comments added

References in corpus (1)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited

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