Regularity theory for fully nonlinear integro-differential equations

✍ Scribed by Luis Caffarelli; Luis Silvestre

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 312 KB
• Volume: 62
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.20274

✦ Synopsis

Abstract

We consider nonlinear integro‐differential equations like the ones that arise from stochastic control problems with purely jump Lévy 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 2, so they can be seen as a natural extension of the regularity theory for elliptic partial differential equations. © 2008 Wiley Periodicals, Inc.