  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.
