TY - GEN A1 - Kraus, Christiane T1 - The degenerate and non-degenerate Stefan problem with inhomogeneous and anisotropic Gibbs-Thomson law N2 - The Stefan problem is coupled with a spatially inhomogeneous and anisotropic Gibbs-Thomson condition at the phase boundary. We show the long-time existence of weak solutions for the non-degenerate Stefan problem with a spatially inhomogeneous and anisotropic Gibbs-Thomson law and a conditional existence result for the corresponding degenerate Stefan problem. To this end, approximate solutions are constructed by means of variational problems for energy functionals with spatially inhomogeneous and anisotropic interfacial energy. By passing to the limit, we establish solutions of the Stefan problem with a spatially inhomogeneous and anisotropic Gibbs--Thomson law in a weak generalized BV-formulation. KW - Stefan problem KW - phase transitions KW - Gibbs-Thomson law KW - free boundaries KW - variational problems KW - geometric measure-theory Y1 - 2015 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/839 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8390 ER -