Regularity theory for fully nonlinear integro-differential equations

Details Regularity theory for fully nonlinear integro-differential equations Regularity theory for fully nonlinear integro-differential equations

2007-09-28

arxiv.org/abs/0709.4681v3

Mathematics

Analysis of PDEs

Minor typos corrected, and some extra comments added

Scientific paper

10.1002/cpa.20274

We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump L\`evy 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.

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