REGULARITY AND EXISTENCE OF SOLUTIONS TO PARABOLIC EQUATIONS WITH NONSTANDARD p(x, t), q(x, t)-GROWTH CONDITIONS

被引：1

作者：

El Bahja, Hamid ^{[1
]}

机构：

[1] African Inst Math Sci, Cape Town, South Africa

来源：

OPUSCULA MATHEMATICA | 2023年 / 43卷 / 06期

关键词：

existence theory; nonlinear parabolic problems; nonstandard growth; regularity theory; CALCULUS; GROWTH;

D O I：

10.7494/OpMath.2023.43.6.759

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard p (x, t), q(x, t)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time L-infinity bounds for the weak solutions.

引用

页码：759 / 788

页数：30

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