Work

A transmission problem arising from the two-phase Stefan problem

Year: 2026

Type: preprint

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 $C^{1,α}$ estimates up to the interface from both sides. These results can be used to obtain $C^{1,α}$ regularity of flat free boundaries for the two-phase Stefan problem with distributed sources.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.24734

Authors: Ferrari, Fausto, Giovagnoli, Davide, Jesus, David

Institutions: University of Bologna, King Abdullah University of Science and Technology

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Università di Bologna

OpenAlex ID: W7204239286

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