Regularity of weak solutions and supersolutions to the porous medium equation

被引：5

作者：

Boegelein, Verena ^{[1
]}

Lehtelae, Pekka ^{[2
]}

Sturm, Stefan ^{[1
]}

机构：

[1] Univ Salzburg, Fachbereich Math, Hellbrunner Str 34, A-5020 Salzburg, Austria

[2] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 185卷

关键词：

Porous medium equation; Weak solutions; Weak supersolutions; Gradient estimates; Obstacle problem;

D O I：

10.1016/j.na.2018.10.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions u(m) is an element of L-loc(2) (0, T; H-loc(1) (Omega)) and u(m+1/2) is an element of L-loc(2) (0, T; H-1 (Omega)) in the definition of weak solutions. Our proof is based on approximation by solutions to obstacle problems. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：49 / 67

页数：19

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