Matzoh ball soup: Heat conductors with a stationary isothermic surface

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)931-946
Number of pages16
JournalAnnals of Mathematics
Volume156
Issue number3
DOIs
Publication statusPublished - 2002 Nov

Keywords

  • Heat equation
  • Overdetermined problems
  • Stationary surfaces

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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