Abstract. We provide existence of a unique smooth solution for a class of one-and two-phase Stefan problems with Gibbs-Thomson correction in arbitrary space dimensions. In addition, it is shown that the moving interface depends analytically on the temporal and spatial variables. Of crucial importance for the analysis is the property of maximal L pregularity for the linearized problem, which is fully developed in this paper as well.

We construct for an equivariant homology theory for proper equivariant CW -complexes an equivariant Chern character under certain conditions. This applies for instance to the sources of the assembly maps in the Farrell-Jones Conjecture with respect to the family F of finite subgroups and in the Baum-Connes Conjecture. Thus we get an explicit calculation of Q ⊗ Z Kn(RG) and Q ⊗ Z Ln(RG) for a commutative ring R with Q ⊂ R and of Q ⊗ Z K top n (C * r (G, F )) for F = R, C in terms of group homology, provided the Farrell-Jones Conjecture with respect to F resp. the Baum-Connes Conjecture is true.

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