Compact embedding for p(x, t)-Sobolev spaces and existence theory to parabolic equations with p(x, t)-growth

被引：12

作者：

Erhardt, Andre H. ^{[1
]}

机构：

[1] Univ Hohenheim, Inst Appl Math & Stat, Emil Wolff Str 27, D-70599 Stuttgart, Germany

来源：

REVISTA MATEMATICA COMPLUTENSE | 2017年 / 30卷 / 01期

关键词：

Existence theory; Nonlinear parabolic problems; Nonstandard growth; Nonstandard parabolic Lebesgue and Sobolev spaces; Compactness theorem; HIGHER INTEGRABILITY; NONSTANDARD GROWTH; VARIABLE EXPONENT; SYSTEMS; ORDER;

D O I：

10.1007/s13163-016-0211-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the compact embedding of p(x, t)-Sobolev spaces into p(x, t)-Lebesgue spaces. Moreover, we prove some existence results for nonlinear parabolic problems of the form partial derivative(t)u - div a(x, t, Du) = f - div (vertical bar F vertical bar F-p(x,F- t)-2) in Omega(T), where the vector-field a(x, t, .) satisfies certain p(x, t)-growth conditions.

引用

页码：35 / 61

页数：27

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