Sharp Regularity Results on Second Derivatives of Solutions to the Monge-Ampere Equation with VMO Type Data

被引：11

作者：

Huang, Qingbo ^{[1
]}

机构：

[1] Wright State Univ, Dept Math & Stat, Dayton, OH 45435 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：

ELLIPTIC-EQUATIONS; INTERIOR;

D O I：

10.1002/cpa.20272

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish interior estimates for L(p)-norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge-Ampere equation det D(2)u = f(x) with zero boundary value, where f(x) is strictly positive, bounded, and satisfies a VMO-type condition. These estimates develop the regularity theory of the Monge-Ampere equation in VMO-type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W(2,p)-estimates. (C) 2008 Wiley Periodicals, Inc.

引用

页码：677 / 705

页数：29

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