Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents

被引：10

作者：

Kozhevnikova, L. M. ^{[1
,2
]}

机构：

[1] Bashkir State Univ, Sterlitamak Branch, Sterlitamak, Russia

[2] Kazan Volga Reg Fed Univ, Elabuga Branch, Yelabuga, Russia

来源：

SBORNIK MATHEMATICS | 2019年 / 210卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

anisotropic elliptic equation; entropy solution; renormalized solution; existence of a solution; variable exponent; Dirichlet problem; EXISTENCE;

D O I：

10.1070/SM9078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in L-1. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration.

引用

页码：417 / 446

页数：30

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