Motivated by the classical model for the binary alloy solidification (crystallization) problem, we show the local in time existence and uniqueness of solutions to a parabolic system strongly coupled through free boundary conditions of Stefan type. Using a modification of the standard change of variables method and coercive estimates in a weighted Hölder space (the weight being a power of $t$) we obtain solutions with maximal global regularity (having at least equal regularity for $t>0$ as at the initial moment).
"Classical solutions to parabolic systems with free boundary of Stefan type." Adv. Differential Equations 10 (12) 1345 - 1388, 2005.