Optimal regularity for phase transition problems with convection
Aram Karakhanyan · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2014
In this paper we consider a steady state phase transition problem with given convection \mathbf v . We prove, among other things, that the weak solution is locally Lipschitz continuous provided that \mathbf{v} = D\xi and ξ is a harmonic function. Moreover, for continuous casting problem, i.e. when \mathbf v is constant vector, we show that Lipschitz free boundaries are C^{1} regular surfaces.