Mucha, Piotr Boguslaw On weak solutions to the Stefan problem with Gibbs-Thomson correction. (English) Zbl 1212.35514 Differ. Integral Equ. 20, No. 7, 769-792 (2007). Summary: The paper investigates the well posedness of the quasi-stationary Stefan problem with the Gibbs-Thomson correction. The main result proves the existence of unique weak solutions provided the initial surface belongs to the \(W_p^{2-3/p}\)-Sobolev-Slobodeckij class for \(p>n+3\), only. The proof is based on Schauder-type estimates in \(L_p\)-type spaces for a linearization of the original system in a rigid domain. Cited in 5 Documents MSC: 35R35 Free boundary problems for PDEs 35K55 Nonlinear parabolic equations 35K99 Parabolic equations and parabolic systems 80A22 Stefan problems, phase changes, etc. 74N20 Dynamics of phase boundaries in solids Keywords:quasi-stationary Stefan problem; Gibbs-Thomson correction; well posedness; Sobolev-Slobodeckij class PDF BibTeX XML Cite \textit{P. B. Mucha}, Differ. Integral Equ. 20, No. 7, 769--792 (2007; Zbl 1212.35514)