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

共 50 条

[21] Higher integrability for obstacle problem related to the singular porous medium equation
Li, Qifan
BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)
[22] GLOBAL HIGHER INTEGRABILITY OF SOLUTIONS TO SUBELLIPTIC DOUBLE OBSTACLE PROBLEMS
Du, Guangwei
Li, Fushan
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (03): : 1021 - 1032
[23] HIGHER INTEGRABILITY FOR GRADIENTS OF SOLUTIONS TO DEGENERATE PARABOLIC SYSTEMS
Le, Dung
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 26 (02) : 597 - 608
[24] Regularity of weak solutions and supersolutions to the porous medium equation
Boegelein, Verena
Lehtelae, Pekka
Sturm, Stefan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 185 : 49 - 67
[25] WEAK SOLUTIONS OF THE POROUS-MEDIUM EQUATION IN A CYLINDER
DAHLBERG, BEJ
KENIG, CE
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 336 (02) : 701 - 709
[26] Higher Integrability for Very Weak Solutions of Inhomogeneous A-Harmonic Form Equations
Tong, Yuxia
Zheng, Shenzhou
Gu, Jiantao
JOURNAL OF APPLIED MATHEMATICS, 2014,
[27] On the higher integrability of weak solutions to the generalized Stokes system with bounded measurable coefficients
Kaplicky, P.
Wolf, J.
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2018, 15 (02) : 127 - 146
[28] Boundary higher integrability for the gradient of distributional solutions of nonlinear systems
Giachetti, D
Schianchi, R
STUDIA MATHEMATICA, 1997, 123 (02) : 175 - 184
[29] BOUNDEDNESS AND INTEGRABILITY PROPERTIES OF WEAK SOLUTIONS OF QUASILINEAR ELLIPTIC-SYSTEMS
MEIER, M
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1982, 333 : 191 - 220
[30] Global integrability for solutions to quasilinear elliptic systems with degenerate coercivity
Li, Ya
Liu, Gaoyang
Gao, Hongya
MATHEMATISCHE NACHRICHTEN, 2024, 297 (05) : 1818 - 1830

← 1 2 3 4 5 →