GLOBAL HIGHER INTEGRABILITY OF WEAK SOLUTIONS OF POROUS MEDIUM SYSTEMS

被引：6

作者：

Moring, Kristian ^{[1
]}

Scheven, Christoph ^{[2
]}

Schwarzacher, Sebastian ^{[3
]}

Singer, Thomas ^{[4
]}

机构：

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

[2] Univ Duisburg Essen, Fak Math, Thea Leymann Str 9, D-45127 Essen, Germany

[3] Univ Karlovy, Katedra Matemat Anal, Matemat Fyzikalni Fak, Sokolovska 83, Prague 18675 8, Czech Republic

[4] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 03期

关键词：

Porous medium type systems; higher integrability; gradient estimates; DEGENERATE PARABOLIC EQUATIONS; SELF-IMPROVING PROPERTY; PARTIAL REGULARITY;

D O I：

10.3934/cpaa.2020069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by partial derivative(t)u - Delta(vertical bar u vertical bar(m-1)u) = div F, where m > 1. More precisely, we prove that under suitable assumptions the spatial gradient D(vertical bar u vertical bar(m-1)u) of any weak solution is integrable to a larger power than the natural power 2. Our analysis includes both the case of the lateral boundary and the initial boundary.

引用

页码：1697 / 1745

页数：49

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