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

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1112-1119
Number of pages8
JournalJournal of Differential Equations
Volume248
Issue number5
DOIs
Publication statusPublished - 2010 Mar 1
Externally publishedYes

Keywords

  • Heat equation
  • Hyperplanes
  • Monge-Ampère-type equation
  • Overdetermined problems
  • Stationary isothermic surfaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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