Matzoh ball soup: Heat conductors with a stationary isothermic surface

被引：32

作者：

Magnanini, R ^{[1
]}

Sakaguchi, S

机构：

[1] Univ Florence, Florence, Italy

[2] Ehime Univ, Matsuyama, Ehime 790, Japan

来源：

ANNALS OF MATHEMATICS | 2002年 / 156卷 / 03期

关键词：

heat equation; overdetermined problems; stationary surfaces;

D O I：

10.2307/3597287

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a bounded heat conductor that satisfies the exterior sphere condition. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1. We show that if the conductor contains a proper sub-domain, satisfying the interior cone condition and having constant boundary temperature at each given time, then the conductor must be a ball.

引用

页码：931 / 946

页数：16

共 25 条

[1]

Aleksandrov A. D., 1958, VESTNIK LENINGRAD U, V13, P5

[2] MATZOH BALL SOUP - A SYMMETRY RESULT FOR THE HEAT-EQUATION [J].

ALESSANDRINI, G .

JOURNAL D ANALYSE MATHEMATIQUE, 1990, 54 :229-236

[3]

ALESSANDRINI G, 1991, APPL ANAL, V40, P251

[4] ON EXTENSIONS OF BRUNN-MINKOWSKI AND PREKOPA-LEINDLER THEOREMS, INCLUDING INEQUALITIES FOR LOG CONCAVE FUNCTIONS, AND WITH AN APPLICATION TO DIFFUSION EQUATION [J].

BRASCAMP, HJ ;

LIEB, EH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 22 (04) :366-389

[5]

DEBRULIN NG, 1958, ASYMPTOTIC METHODS A, V4

[6]

Evans L.C., 2010, Partial differential equations, DOI DOI 10.1090/GSM/019

[7]

EVANS LC, 1985, ANN I H POINCARE-AN, V2, P1

[8]

Freidlin M I, 2012, Fundamental Principles of Mathematical Sciences, V260

[9]

Gallot S., 1993, RIEMANNIAN GEOMETRY

[10]

GILBARG D, 1983, ELLOPTIC PARTIAL DIF

← 1 2 3 →