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.
Matzoh ball soup: heat conductors with a stationary isothermic surface / R. MAGNANINI; SAKAGUCHI S.. - In: ANNALS OF MATHEMATICS. - ISSN 0003-486X. - STAMPA. - 156:(2002), pp. 941-956.
Matzoh ball soup: heat conductors with a stationary isothermic surface
MAGNANINI, ROLANDO;
2002
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.File in questo prodotto:
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