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arXiv · 2608.24734

A transmission problem arising from the two-phase Stefan problem

Fausto Ferrari·Davide Giovagnoli·David Jesus
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Abstract

We study a parabolic transmission problem whose interface condition depends on the time derivative of the solution. This model arises naturally as the linearized limiting profile of a two-phase inhomogeneous Stefan problem after the hodograph transform. Our main result shows the existence and uniqueness of a classical solution. We also prove a Harnack inequality for a general class of transmission problems and establish $C^{1,\alpha}$ estimates up to the interface from both sides. These results can be used to obtain $C^{1,\alpha}$ regularity of flat free boundaries for the two-phase Stefan problem with distributed sources.

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Fausto Ferrari, Davide Giovagnoli, David Jesus. 2026-08-25. A transmission problem arising from the two-phase Stefan problem. https://arxiv.org/abs/2608.24734

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