### On the Stefan problem with surface tension in the $L_p$ framework

Piotr Bogusław Mucha

#### Abstract

We prove the existence of unique regular local in time solutions to the quasi-stationary one-phase Stefan problem with the Gibbs-Thomson correction. The result is optimal with respect to $L_p$ regularity and the obtained phase surface is a submanifold of the $W^{3,1}_p$-class. The proof is based on a Schauder-type estimate for a linearization of the original system.

#### Article information

Source
Adv. Differential Equations Volume 10, Number 8 (2005), 861-900.

Dates
First available in Project Euclid: 18 December 2012

Mucha, Piotr Bogusław. On the Stefan problem with surface tension in the $L_p$ framework. Adv. Differential Equations 10 (2005), no. 8, 861--900.https://projecteuclid.org/euclid.ade/1355867822