Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 62, Issue 5, Pages 597-638Publisher
WILEY
DOI: 10.1002/cpa.20274
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Funding
- National Science Foundation grants.
- Division Of Mathematical Sciences [0901995] Funding Source: National Science Foundation
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We consider nonlinear integro-differential equations like the ones that arise from stochastic control problems with purely jump Levy processes. We obtain a non-local version of the ABP estimate, Harnack inequality, and interior C-1,C-alpha regularity for general fully nonlinear integro-differential equations. Our estimates remain uniform as the degree of the equation approaches 2, so they can be seen as a natural extension of the regularity theory for elliptic partial differential equations. (C) 2008 Wiley Periodicals, Inc.
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