Classical solution of quasi-stationary Stefan problem

This paper considers the quasi-stationary Stefan problem: Delta u(x, t) = 0 in space-time domain, u = 0 and V-nu + partial derivative u/partial derivative nu = 0 on the free boundary. Under the natural conditions the existence of classical solution locally in time is proved by making use of the property of Frechet derivative operator and fixed point theorem. For the sake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can be dealt with in a similar way with more complicated calculation.