Advances in Differential Equations

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

Piotr Bogusław Mucha

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 74N20: Dynamics of phase boundaries 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Mucha, Piotr Bogusław. On the Stefan problem with surface tension in the $L_p$ framework. Adv. Differential Equations 10 (2005), no. 8, 861--900.

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