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

Rolando Magnanini, Shigeru Sakaguchi

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We consider the entire graph S of a continuous real function over RN - 1 with N ≥ 3. Let Ω be a domain in RN with S as a boundary. Consider in Ω the heat flow 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 Ω. 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-Ampère-type equation.

本文言語English
ページ(範囲)1112-1119
ページ数8
ジャーナルJournal of Differential Equations
248
5
DOI
出版ステータスPublished - 2010 3 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

フィンガープリント

「Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル