Parabolic quasi-concavity for solutions to parabolic problems in convex rings

被引：22

作者：

Ishige, Kazuhiro ^{[1
]}

Salani, Paolo ^{[2
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

[2] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

来源：

MATHEMATISCHE NACHRICHTEN | 2010年 / 283卷 / 11期

关键词：

Parabolic equations; convexity; quasi-concavity; LEVEL SETS; BOUNDARY; MINKOWSKI; PRINCIPLE; EQUATIONS;

D O I：

10.1002/mana.200910242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate some geometric properties of level sets of the solutions of parabolic problems in convex rings. We introduce the notion of parabolic quasi-concavity, which involves time and space jointly and is a stronger property than the spatial quasi-concavity, and study the convexity of superlevel sets of the solutions. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1526 / 1548

页数：23

共 50 条

[31] Asymptotic behaviour of the solutions of quasi-linear parabolic problems in perforated domains
Skrypnik, IV
DOKLADY AKADEMII NAUK, 1997, 352 (04) : 466 - 469
[32] On the Quasi-Concavity of Equipment Sharing Games with Perishable Raw Materials
Li, Jun
Cai, Xiaoqiang
Zeng, Yinlian
Feng, Hairong
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING, 2021, 30 (06) : 649 - 666
[33] REPRESENTATION FOR DISTRIBUTIONAL SOLUTIONS OF PARABOLIC PROBLEMS
MEYER, HD
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A145 - A145
[34] Global solutions for quasilinear parabolic problems
Adrian Constantin
Joachim Escher
Journal of Evolution Equations, 2002, 2 : 97 - 111
[35] REPRESENTATION FOR DISTRIBUTIONAL SOLUTIONS OF PARABOLIC PROBLEMS
MEYER, HD
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1977, 8 (02) : 356 - 367
[36] Global solutions for quasilinear parabolic problems
Constantin, A
Escher, J
JOURNAL OF EVOLUTION EQUATIONS, 2002, 2 (01) : 97 - 111
[37] Asymptotics of Fundamental Solutions of Parabolic Problems
Danilov, V. G.
MATHEMATICAL NOTES, 2024, 115 (1-2) : 182 - 191
[38] SOLUTIONS FOR PSEUDO-PARABOLIC PROBLEMS
LYASHKO, SI
IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1985, (09): : 71 - 72
[39] CONVEX SOLUTIONS TO NON-LINEAR ELLIPTIC AND PARABOLIC BOUNDARY-VALUE-PROBLEMS
KOREVAAR, NJ
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1983, 32 (04) : 603 - 614
[40] A CLASS OF PARABOLIC QUASI-LINEAR PROBLEMS
ARTOLA, M
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1986, 5B (01): : 51 - 70

← 1 2 3 4 5 →