New perturbation methods for nonlinear parabolic problems

被引：52

作者：

Kuusi, Tuomo ^{[2
]}

Mingione, Giuseppe ^{[1
]}

机构：

[1] Univ Parma, Dipartimento Matemat, I-43124 Parma, Italy

[2] Aalto Univ, Inst Math, FI-00076 Aalto, Finland

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2012年 / 98卷 / 04期

基金：

芬兰科学院;

关键词：

Degenerate parabolic systems; Regularity; Intrinsic geometry; SINGULAR SET; LIPSCHITZ REGULARITY; HIGHER INTEGRABILITY; REIFENBERG DOMAINS; EQUATIONS; SYSTEMS; FUNCTIONALS; MINIMA; GROWTH;

D O I：

10.1016/j.matpur.2012.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop methods aimed at deriving regularity results for solutions to nonlinear degenerate parabolic equations and systems via local perturbation; as a consequence we obtain, in a unified way, Lipschitz continuity of solutions under weak parabolicity assumptions, and gradient continuity results in borderline cases. Nonlinear Schauder estimates as those of Misawa (2002) [29] are recovered and extended to more general settings. (C) 2012 Elsevier Masson SAS. All rights reserved.

引用

页码：390 / 427

页数：38

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