Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles

被引：35

作者：

Scheven, Christoph ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fac Math, D-45117 Essen, Germany

来源：

MANUSCRIPTA MATHEMATICA | 2015年 / 146卷 / 1-2期

关键词：

HIGHER INTEGRABILITY; UNILATERAL PROBLEMS; ELLIPTIC-EQUATIONS; WEAK SOLUTIONS; GRADIENT; SYSTEMS; REGULARITY; SETS;

D O I：

10.1007/s00229-014-0684-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the concept of localizable solutions of parabolic obstacle problems of p-Laplace-type with highly irregular obstacles and provide corresponding existence results. The main new feature of the constructed solutions is that they solve the problem locally, which is the appropriate notion for the examination of local properties like regularity. As an application, we derive Caldern-Zygmund estimates for the spatial gradient of localizable solutions to parabolic obstacle problems.

引用

页码：7 / 63

页数：57

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