Matzoh ball soup: Heat conductors with a stationary isothermic surface

Rolando Magnanini; Shigeru Sakaguchi

doi:10.2307/3597287

Matzoh ball soup: Heat conductors with a stationary isothermic surface

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journal › Article › peer-review

31 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 language	English
Pages (from-to)	931-946
Number of pages	16
Journal	Annals of Mathematics
Volume	156
Issue number	3
DOIs	https://doi.org/10.2307/3597287
Publication status	Published - 2002 Nov
Externally published	Yes

Keywords

Heat equation
Overdetermined problems
Stationary surfaces

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.2307/3597287

Cite this

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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.",

keywords = "Heat equation, Overdetermined problems, Stationary surfaces",

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AB - 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.

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KW - Overdetermined problems

KW - Stationary surfaces

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Matzoh ball soup: Heat conductors with a stationary isothermic surface

Abstract

Keywords

ASJC Scopus subject areas

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