Resumen de Stationary isothermic surfaces for unbounded domains

Rolando Magnanini , Shigeru Sakaguchi

• 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.