Entropy and Renormalized Solutions for Nonlinear Elliptic Problem Involving Variable Exponent and Measure Data

被引：0

作者：

Mohamed Badr BENBOUBKER ^{[1
]}

Houssam CHRAYTEH ^{[2
]}

Mostafa EL MOUMNI ^{[3
]}

Hassane HJIAJ ^{[3
]}

机构：

[1] National School of Applied Sciences, Abdelmalek Essaadi University

[2] Beirut Arab University, Faculty of Science,Department of Mathematics and Computer Science

[3] Laboratory LAMA, Faculty of Sciences Dhar El Mahraz,Sidi Mohamed Ben Abdellah University

来源：

Acta Mathematica Sinica,English Series | 2015年 / 01期

关键词：

Nonlinear elliptic problem; Sobolev spaces; variable exponent; entropy solution; renormalized solution; measure data;

D O I：

暂无

中图分类号：

O175.25 [椭圆型方程];

学科分类号：

070104 ;

摘要：

We give an existence result of entropy and renormalized solutions for strongly nonlinear elliptic equations in the framework of Sobolev spaces with variable exponents of the type:-div(a(x, u, u) + φ(u)) + g(x, u, u) = μ, where the right-hand side belongs to L1(Ω) + W-1,p(x)(Ω),-div(a(x, u, u)) is a Leray–Lions oper- ator defined from W-1,p(x)(Ω) into its dual and φ∈ C0(R, RN). The function g(x, u, u) is a non linear lower order term with natural growth with respect to |u| satisfying the sign condition, that is,g(x, u, u)u ≥ 0.

引用

页码：151 / 169

页数：19

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