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

共 32 条

[21] Calderon-Zygmund theory for parabolic obstacle problems with nonstandard growth
Erhardt, Andre
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2014, 3 (01) : 15 - 44
[22] Erhardt AH, 2016, ADV DIFFERENTIAL EQU, V21, P463
[23] Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth
Erhardt, Andre H.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 435 (02) : 1772 - 1803
[24] Ettwein F., 2003, GEOMETRIC ANAL NONLI
[25] Evans LC, 2010, Partial Differential Equations
[26] Intrinsic scaling for PDE's with an exponential nonlinearity
Henriques, Eurica
Urbano, Jose Miguel
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (05) : 1701 - 1721
[27] Ruzicka M, 2000, LECT NOTES MATH, V1748, P1
[28] Ruzicka M., 2004, APPL MATH, V49, P565, DOI [DOI 10.1007/S10492-004-6432-8, 10.1007/s10492-004-6432-8]
[29] Showalter RE., 1997, MONOTONE OPERATORS B
[30] Temam R, 2001, Navier-Stokes equations: theory and numerical analysis

← 1 2 3 4 →