A symmetry theorem in two-phase heat conductors

<abstract><p>We consider the Cauchy problem for heat diffusion equation in whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and other 1. Under assumptions that is bounded interface class $ C^{2, \alpha} $, we show if stationary isothermic, then it must be a sphere. The method moving planes due to Serrin directly utilized prove result.</p></abstract>