On localization of solutions of elliptic equations with nonhomogeneous anisotropic degeneracy

被引：22

作者：

Antontsev, SN

Shmarev, SI

机构：

[1] Universidade da Beira Interior, Covilha

[2] Universidad de Oviedo, Oviedo

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2005年 / 46卷 / 05期

关键词：

nonlinear elliptic equation; nonhomogeneous degeneracy; localization of solutions;

D O I：

10.1007/s11202-005-0076-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The work deals with the Dirichlet problem for elliptic equations with nonhomogeneous anisotropic degeneracy in a possibly unbounded domain of multidimensional Euclidean space. The existence of weak solutions is proved. Some conditions are established connecting the character of nonlinearity of the equation and the geometric characteristics of the domain which guarantee the one-dimensional localization (vanishing) of weak solutions. The equation with anisotropic degeneracy is shown to admit localized solutions even in the absence of absorption.

引用

页码：765 / 782

页数：18

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