Gradient estimates for singular fully nonlinear elliptic equations

被引：2
|
作者：
Lieberman, Gary M. [1 ]
机构：
[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 119卷
关键词：
Singular differential equations; Nonlinear partial differential equations; a priori estimates; CONORMAL DERIVATIVE PROBLEM; REGULARITY;
D O I：
10.1016/j.na.2014.10.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a class of singular fully nonlinear elliptic equations under suitable natural conditions, with the model equation being Delta u + b(gamma . Du)/d - u + c vertical bar Du vertical bar(2) = f for Lipschitz functions b > 0, c and f, where d denotes distance to the boundary of the domain and gamma is a suitable extension of the interior unit normal. We show that such equations have a unique, globally C-1 solution (without any a priori prescription of boundary data). (C) 2014 Elsevier Ltd. All rights reserved.
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页码：382 / 397
页数：16
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