Existence of Classical Solution of a Quasilinear Stefan-Signorini Problem

In this paper, we consider an one-phase quasilinear Stefan-Signorini problem. In 1] X. Liu has proved the existence and the uniqueness of this problem by the traditional penalty method (see 3] and 4]). Here we use the Mixed Scheme in 2] which is more suitable to the Stefan-Signorini problem and obtain more natural existence results.