Traces and embeddings of anisotropic function spaces

In this paper we characterize the trace spaces of a class of weighted function spaces of intersection type with mixed regularities. To a large extent we can overcome the difficulty of mixed scales by employing a microscopic improvement in Sobolev and mixed derivative embeddings with fixed integrability. We apply the general results to prove maximal $L^p$-$L^q$-regularity for the linearized, fully inhomogeneous two-phase Stefan problem with Gibbs-Thomson correction.