Matzoh ball soup: heat conductors with a stationary isothermic surface


We consider a bounded heat conductor that satisfied 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.


Rolando Magnanini

Shigeru Sakaguchi