Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
Analysis of PDEs
2025-04-25 v1
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.
Cite
@article{arxiv.2504.17383,
title = {Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem},
author = {Kyeongbae Kim and Ho-Sik Lee and Harsh Prasad},
journal= {arXiv preprint arXiv:2504.17383},
year = {2025}
}