Stationary isothermic surfaces for unbounded domains

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The initial temperature of a heat conductor is zero and its boundary temperature is kept equal to one at each time. The conductor contains a stationary isothermic surface, that is, an invariant spatial level surface of the temperature. In a previous paper, we proved that, if the conductor is bounded, then it must be a ball. Here, we prove that the boundary of the conductor is either a hyperplane or the union of two parallel hyperplanes when it is unbounded and satisfies certain global assumptions.

Original languageEnglish
Pages (from-to)2723-2738
Number of pages16
JournalIndiana University Mathematics Journal
Issue number6
Publication statusPublished - 2007
Externally publishedYes


  • Isoparametric surfaces
  • Overdetermined problems
  • Stationary surfaces

ASJC Scopus subject areas

  • Mathematics(all)


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