Regularity for parabolic equations with time dependent growth

被引：9

作者：

Ok, Jihoon ^{[1
,2
]}

机构：

[1] Kyung Hee Univ, Dept Appl Math, Yongin 17104, South Korea

[2] Kyung Hee Univ, Inst Nat Sci, Yongin 17104, South Korea

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 120卷

关键词：

Parabolic p-Laplacian; Holder continuity; Variable exponent space; Time dependent growth; HOLDER CONTINUITY; VARIABLE EXPONENT; NONSTANDARD GROWTH; ELLIPTIC-EQUATIONS; WEAK SOLUTIONS; GENERAL-CLASS; GRADIENT; FUNCTIONALS; MINIMIZERS; SYSTEMS;

D O I：

10.1016/j.matpur.2018.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the regularity theory for parabolic equations of the p-Laplace type, where p = p(t) is a function of the time variable t. In particular, we prove Holder continuity of the spatial gradient for weak solutions under a sharp regularity condition on p(t), which is the log-Holder continuity. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：253 / 293

页数：41

共 48 条

[1]

Acerbi E, 2005, J REINE ANGEW MATH, V584, P117

[2] Regularity results for parabolic systems related to a class of non-Newtonian fluids [J].

Acerbi, E ;

Mingione, G ;

Seregin, GA .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (01) :25-60

[3] Regularity results for a class of functionals with non-standard growth [J].

Acerbi, E ;

Mingione, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) :121-140

[4]

Alkhutov YA., 2011, J Math Sci, V179, P347, DOI [10.1007/s10958-011-0599-9, DOI 10.1007/S10958-011-0599-9]

[5]

[Anonymous], 2003, DIRECT METHODS CALCU, DOI DOI 10.1142/5002

[6]

[Anonymous], 1996, 2 ORDER PARABOLIC DI, DOI DOI 10.1142/3302

[7]

[Anonymous], 1993, DEGENERATE PARABOLIC, DOI DOI 10.1007/978-1-4612-0895-2

[8] The Cauchy-Dirichlet problem for a general class of parabolic equations [J].

Baroni, Paolo ;

Lindfors, Casimir .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (03) :593-624

[9] Calderon-Zygmund estimates for parabolic p(x, t)-Laplacian systems [J].

Baroni, Paolo ;

Boegelein, Verena .

REVISTA MATEMATICA IBEROAMERICANA, 2014, 30 (04) :1355-1386

[10] Holder estimates for parabolic p(x, t)-Laplacian systems [J].

Boegelein, Verena ;

Duzaar, Frank .

MATHEMATISCHE ANNALEN, 2012, 354 (03) :907-938

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