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
收藏
页码：1112 / 1119
页数：8
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