On solutions to Dirichlet problems involving the infinity-Laplacian

被引：29

作者：

Bhattacharya, Tilak ^{[1
]}

Mohammed, Ahmed ^{[2
]}

机构：

[1] Western Kentucky Univ, Dept Math & Comp Sci, Bowling Green, KY 42101 USA

[2] Ball State Univ, Dept Math Sci, Muncie, IN 47306 USA

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2011年 / 4卷 / 04期

关键词：

Infinity-Laplacian; comparison principle; Dirichlet problems; singular boundary value problem; VISCOSITY SOLUTIONS;

D O I：

10.1515/ACV.2010.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under appropriate conditions on f(x, t), we prove the existence of viscosity solutions to Delta(infinity)u = f(x, u) that take prescribed continuous data on the boundary of bounded domains. As an application, singular boundary value problems are investigated. These problems are shown to admit viscosity solutions and their asymptotic behavior near the boundary is analyzed. Maximum and comparison principles are used as the main tools in these investigations.

引用

页码：445 / 487

页数：43

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