Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space

被引：7

作者：

Magnanini, Rolando ^{[1
]}

Sakaguchi, Shigeru ^{[2
]}

机构：

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

[2] Hiroshima Univ, Grad Sch Engn, Dept Appl Math, Higashihiroshima 7398527, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 05期

基金：

日本学术振兴会;

关键词：

Heat equation; Overdetermined problems; Stationary isothermic surfaces; Hyperplanes; Monge-Ampere-type equation;

D O I：

10.1016/j.jde.2009.11.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the entire graph S of a continuous real function over R(N-1) with N >= 3. Let Omega be a domain in R(N) with S as a boundary. Consider in Omega the beat now with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in Omega. We show that S must be a hyperplane under some general conditions on S. This is related to Liouville or Bernstein-type theorems for some elliptic Monge-Ampere-type equation. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：1112 / 1119

页数：8

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