Differential and Integral Equations

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

Piotr Bogusław Mucha

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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

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

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35D05 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


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

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