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arXiv · 2504.17383

Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem

Kyeongbae Kim·Ho-Sik Lee·Harsh Prasad
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Abstract

We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in time, is scaling deficient and influenced by far-off effects. We study the the problem in a geometry adapted to the solution and obtain oscillation estimates in intrinsically scaled cylinders. Furthermore, via certain uniform estimates, we construct a continuous weak solution to the corresponding initial boundary value problem with a quantitative modulus of continuity.

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Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad. 2025-04-24. Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem. https://arxiv.org/abs/2504.17383

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