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

[1] BROWNIAN-MOTION IN A CONVEX RING AND QUASI-CONCAVITY
BORELL, C
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 86 (01) : 143 - 147
[2] 9 KINDS OF QUASI-CONCAVITY AND CONCAVITY
DIEWERT, WE
AVRIEL, M
ZANG, I
JOURNAL OF ECONOMIC THEORY, 1981, 25 (03) : 397 - 420
[3] Parabolic power concavity and parabolic boundary value problems
Ishige, Kazuhiro
Salani, Paolo
MATHEMATISCHE ANNALEN, 2014, 358 (3-4) : 1091 - 1117
[4] Parabolic power concavity and parabolic boundary value problems
Kazuhiro Ishige
Paolo Salani
Mathematische Annalen, 2014, 358 : 1091 - 1117
[5] NOTE ON SEPARABILITY AND QUASI-CONCAVITY
YAARI, ME
ECONOMETRICA, 1977, 45 (05) : 1183 - 1186
[6] Spatial concavity of solutions to parabolic systems
Ishige, Kazuhiro
Nakagawa, Kazushige
Salani, Paolo
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2020, 20 (01) : 291 - 313
[7] OTHER DETERMINENTAL CONDITIONS FOR CONCAVITY AND QUASI-CONCAVITY
LEROUX, A
JOURNAL OF MATHEMATICAL ECONOMICS, 1984, 13 (01) : 43 - 49
[8] Local quasi-concavity of the solutions of the heat equation with a nonnegative potential
Andreucci, Daniele
Ishige, Kazuhiro
ANNALI DI MATEMATICA PURA ED APPLICATA, 2013, 192 (03) : 329 - 348
[9] Is quasi-concavity preserved by heat flow?
Kazuhiro Ishige
Paolo Salani
Archiv der Mathematik, 2008, 90 : 450 - 460
[10] Local quasi-concavity of the solutions of the heat equation with a nonnegative potential
Daniele Andreucci
Kazuhiro Ishige
Annali di Matematica Pura ed Applicata, 2013, 192 : 329 - 348

← 1 2 3 4 5 →