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.
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页码：3148 / 3190
页数：43
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