Logarithmic Continuity for the Nonlocal Degenerate Two-Phase Stefan Problem
Abstract
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 is influenced by far-off effects. We study 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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 823–867
- Publication date
- 4 March 2026
- Language
- EN