Obstacle problem for a class of parabolic equations of generalized p-Laplacian type

被引：5

作者：

Lindfors, Casimir ^{[1
]}

机构：

[1] Aalto Univ, Inst Math, POB 11100, FI-00076 Aalto, Finland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 10期

基金：

芬兰科学院;

关键词：

Degenerate/singular parabolic equations; General growth conditions; Obstacle problem; GROWTH-CONDITIONS; GRADIENT REGULARITY; BOUNDARY; SUPERSOLUTIONS; MINIMIZERS; DEGENERATE;

D O I：

10.1016/j.jde.2016.08.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and that a uniformly bounded sequence of weak supersolutions converges to a weak supersolution. Moreover, we prove that if the obstacle is continuous, so is the solution. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：5499 / 5540

页数：42

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