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
Piotr Bogusław Mucha. "On the Stefan problem with surface tension in the $L_p$ framework." Adv. Differential Equations 10 (8) 861 - 900, 2005. https://doi.org/10.57262/ade/1355867822
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