Analytic Solutions for the Stefan Problem with Gibbs-Thomson Correction

Stefan problems are widely used to model the freezing/melting process of water/ice. In this talk a general existence and uniqeness result of classical solutions for a class of Stefan problems with Gibbs-Thomson correction in arbitray space dimensions is provided. In addition, it will be shown that the moving boundary depends analytically on the temporal and spatial variables. Of crucial importance for the analysis is the property of maximal Lp-regularity for the linearized problem, which is based on the Dore-Venni theorem.