Regularity Theory for Fully Nonlinear Integro-Differential Equations

被引：426

作者：

Caffarelli, Luis ^{[1
]}

Silvestre, Luis ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2009年 / 62卷 / 05期

基金：

美国国家科学基金会;

关键词：

HARNACK INEQUALITIES; VISCOSITY SOLUTIONS; UNIQUENESS; OPERATORS;

D O I：

10.1002/cpa.20274

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：597 / 638

页数：42

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