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2007 On weak solutions to the Stefan problem with Gibbs-Thomson correction
Piotr Bogusław Mucha
Differential Integral Equations 20(7): 769-792 (2007).

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.

Citation

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Piotr Bogusław Mucha. "On weak solutions to the Stefan problem with Gibbs-Thomson correction." Differential Integral Equations 20 (7) 769 - 792, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35514
MathSciNet: MR2333656

Subjects:
Primary: 35R35
Secondary: 35B30, 35D05, 80A22

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 7 • 2007
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