Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

Yongqiang Fu; Miaomiao Yang

doi:10.1186/1029-242X-2014-23

Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

Yongqiang Fu
, Miaomiao Yang^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

This paper is concerned with the following Dirichlet problem for a quasilinear elliptic system with variable growth: - divσ(x, u(x),Du(x)) = f in Ω, u(x) = 0 on ∂Ω, where ΩC Rn is a bounded domain. By means of the Young measure and the theory of variable exponent Sobolev spaces, we obtain the existence of solutions in W₀^1,p(x) (Ω,R^m) for each f ε (W₀^1,p(x) (Ω,R^m)).

Original language	English
Article number	23
Journal	Journal of Inequalities and Applications
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1186/1029-242X-2014-23
State	Published - Jan 2014

Keywords

Monotone operator
Quasilinear elliptic system
Variable exponent
Young measure

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10.1186/1029-242X-2014-23

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title = "Existence of solutions for quasilinear elliptic systems in divergence form with variable growth",

abstract = "This paper is concerned with the following Dirichlet problem for a quasilinear elliptic system with variable growth: - divσ(x, u(x),Du(x)) = f in Ω, u(x) = 0 on ∂Ω, where ΩC Rn is a bounded domain. By means of the Young measure and the theory of variable exponent Sobolev spaces, we obtain the existence of solutions in W01,p(x) (Ω,Rm) for each f ε (W01,p(x) (Ω,Rm)).",

keywords = "Monotone operator, Quasilinear elliptic system, Variable exponent, Young measure",

author = "Yongqiang Fu and Miaomiao Yang",

year = "2014",

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doi = "10.1186/1029-242X-2014-23",

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T1 - Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

AU - Fu, Yongqiang

AU - Yang, Miaomiao

PY - 2014/1

Y1 - 2014/1

N2 - This paper is concerned with the following Dirichlet problem for a quasilinear elliptic system with variable growth: - divσ(x, u(x),Du(x)) = f in Ω, u(x) = 0 on ∂Ω, where ΩC Rn is a bounded domain. By means of the Young measure and the theory of variable exponent Sobolev spaces, we obtain the existence of solutions in W01,p(x) (Ω,Rm) for each f ε (W01,p(x) (Ω,Rm)).

AB - This paper is concerned with the following Dirichlet problem for a quasilinear elliptic system with variable growth: - divσ(x, u(x),Du(x)) = f in Ω, u(x) = 0 on ∂Ω, where ΩC Rn is a bounded domain. By means of the Young measure and the theory of variable exponent Sobolev spaces, we obtain the existence of solutions in W01,p(x) (Ω,Rm) for each f ε (W01,p(x) (Ω,Rm)).

KW - Monotone operator

KW - Quasilinear elliptic system

KW - Variable exponent

KW - Young measure

UR - https://www.scopus.com/pages/publications/84899817732

U2 - 10.1186/1029-242X-2014-23

DO - 10.1186/1029-242X-2014-23

M3 - 文章

AN - SCOPUS:84899817732

SN - 1025-5834

VL - 2014

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 23

ER -

Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

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Keywords

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