COMPACT EMBEDDINGS FOR SOBOLEV SPACES OF VARIABLE EXPONENTS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN AND ITS CRITICAL EXPONENT

被引：0

作者：

Mizuta, Yoshihiro ^{[1
]}

Ohno, Takao ^{[2
]}

Shimomura, Tetsu ^{[3
]}

Shioji, Naoki ^{[4
]}

机构：

[1] Hiroshima Univ, Dept Math, Grad Sch Sci, Higashihiroshima 7398521, Japan

[2] Hiroshima Natl Coll Maritime Technol, Osakikamijima, Hiroshima 7250231, Japan

[3] Hiroshima Univ, Dept Math, Grad Sch Educ, Higashihiroshima 7398524, Japan

[4] Yokohama Natl Univ, Dept Math, Hodogaya Ku, Yokohama, Kanagawa 2408501, Japan

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2010年 / 35卷 / 01期

关键词：

Sobolev spaces of variable exponents; compact embeddings; nonlinear elliptic problems; GENERALIZED LEBESGUE; RIESZ-POTENTIALS; EQUATIONS; TOPOLOGY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a sufficient condition for the compact embedding from W-0(k,p(.))(Omega) to L-q(.)(Omega) in case ess in f(x epsilon Omega)(Np(x)/(N - kp(x)) - q(x)) = 0, where Omega is a bounded open set in R-N. As an application, we find a nontrivial nonnegative weak solution of the nonlinear elliptic equation -div (|del u(x)|(p(x)-2)del u(x)) = |u(x)|(q(x)-2)u(x) = in Omega, u(x) = 0 on partial derivative Omega. We also consider the existence of a weak solution to the problem above even if the embedding is not compact.

引用

页码：115 / 130

页数：16

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