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2005 On the Stefan problem with surface tension in the $L_p$ framework
Piotr Bogusław Mucha
Adv. Differential Equations 10(8): 861-900 (2005).

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.

Citation

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Piotr Bogusław Mucha. "On the Stefan problem with surface tension in the $L_p$ framework." Adv. Differential Equations 10 (8) 861 - 900, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1106.35148
MathSciNet: MR2150869

Subjects:
Primary: 35R35
Secondary: 35J05, 74N20, 80A22

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 8 • 2005
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