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Matzoh Ball Soup: Heat Conductors with a Stationary Isothermic Surface

Rolando Magnanini and Shigeru Sakaguchi
Annals of Mathematics
Second Series, Vol. 156, No. 3 (Nov., 2002), pp. 931-946
Published by: Annals of Mathematics
DOI: 10.2307/3597287
Stable URL: http://www.jstor.org/stable/3597287
Page Count: 16
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Matzoh Ball Soup: Heat Conductors with a Stationary Isothermic Surface
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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.

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