NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT GROWTH IN NONSMOOTH DOMAINS

被引：18

作者：

Byun, Sun-Sig ^{[1
,2
]}

Ok, Jihoon ^{[3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Sch Math, Seoul 02455, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2016年 / 48卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

nonlinear parabolic equation; p(center dot)-Laplacian; L-q(center dot)-estimate; ELLIPTIC-EQUATIONS; HIGHER INTEGRABILITY; NONSTANDARD GROWTH; ZYGMUND THEORY; WEAK SOLUTIONS; REGULARITY; GRADIENT; FUNCTIONALS; COEFFICIENTS;

D O I：

10.1137/16M1056298

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Calderon-Zygmund theory for nonlinear parabolic problems in the setting of the variable exponent Lebesgue spaces. In particular, we prove the global L-s(center dot) integrability of the gradient of solutions to parabolic equations with p(center dot) growth in nonsmooth domains with s(center dot) > p(center dot). In addition, we present precise regularity conditions on the variable exponent functions, the nonlinearity, and the boundary of a domain to enable us to obtain the desired result.

引用

页码：3148 / 3190

页数：43

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