## 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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039409

Mathematical Reviews number (MathSciNet)
MR2333656

Zentralblatt MATH identifier
1212.35514

#### Citation

Mucha, Piotr Bogusław. On weak solutions to the Stefan problem with Gibbs-Thomson correction. Differential Integral Equations 20 (2007), no. 7, 769--792. https://projecteuclid.org/euclid.die/1356039409