Holder continuity of solutions of an elliptic equation uniformly degenerating on part of the domain

被引：9

作者：

Alkhutov, Yu. A. ^{[1
]}

Guseinov, S. T.

机构：

[1] Vladimir State Pedag Univ, Vladimir, Russia

来源：

DIFFERENTIAL EQUATIONS | 2009年 / 45卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Elliptic Equation; Sobolev Inequality; Ellipticity Condition; Cauchy Inequality; Oscillation Property;

D O I：

10.1134/S0012266109010066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a second-order divergence elliptic equation in a domain D divided by a hyperplane in two parts. The equation is uniformly elliptic in one of these parts and is uniformly degenerate with respect to a small parameter E > in the other. We show that each solution is Holder continuous in D with Holder exponent independent of E >.

引用

页码：53 / 58

页数：6