A comparison principle for the porous medium equation and its consequences

被引：9

作者：

Avelin, Benny ^{[1
,2
]}

Lukkari, Teemu ^{[1
]}

机构：

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

[2] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2017年 / 33卷 / 02期

基金：

瑞典研究理事会; 芬兰科学院;

关键词：

Porous medium equation; PME; elliptic comparison principle; obstacle problem; parabolic capacity; DEGENERATE; SUPERSOLUTIONS;

D O I：

10.4171/RMI/950

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a comparison principle for the porous medium equation in more general open sets in Rn+1 than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.

引用

页码：573 / 594

页数：22

共 20 条

[1]

ALT HW, 1983, MATH Z, V183, P311

[2]

[Anonymous], 1969, Lectures on Analysis

[3]

[Anonymous], 2007, POROUS MEDIUM EQUATI

[4] LOWER SEMICONTINUITY OF WEAK SUPERSOLUTIONS TO THE POROUS MEDIUM EQUATION [J].