Existence of a Classical Solution for a Multidimensional Filtration Problem

We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set {u=0}) of a multidimensional filtration problem. The key point to get the regularity of the level set {u=0} is the proof of an a priori estimate for the L_∞-norm of u_t. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.