Analytic solutions for a Stefan problem with Gibbs-Thomson correction
Joachim Escher, Jan W. Prüss, Gieri Simonett · Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover) · 2003
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-p-regularity for the linearized problem, which is fully developed in this paper as well.