## Differential and Integral Equations

### On weak solutions to the Stefan problem with Gibbs-Thomson correction

Piotr Bogusław Mucha

#### Abstract

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 $W^{2-3/p}_p$-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.

#### Article information

Source
Differential Integral Equations Volume 20, Number 7 (2007), 769-792.

Dates
First available in Project Euclid: 20 December 2012