Year: 2026
Type: article
Abstract: We consider the one-phase Stefan problem describing the evolution of melting ice. On the one hand, we focus on understanding the evolution of the free boundary near isolated singular points, and we establish for the first time upper and (more surprisingly) lower estimates for its evolution. In 2D, these bounds almost match the best known ones for radial solutions, but hold for all solutions to the Stefan problem, with no extra assumption on the initial or boundary data. On the other hand, as a consequence of our results, we also characterize the global regularity of the free boundary, as follows: it can be written as a graph { t = Γ ( x ) } \{t=\Gamma (x)\} , where Γ \Gamma is C 1 C^1 (and not C 2 C^2 ) near any singular points in the lower strata Σ m \Sigma _m , m ≤ n − 2 m\leq n-2 . Moreover, Γ \Gamma is not C 1 C^1 at singular points in Σ n − 1 \Sigma _{n-1} .
DOI: 10.1090/tran/9630
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1066208, G1074888338, G1133822655, G128764640, G1465780022, G1549693833, G1776134997, G1805859637, G1825059740, G1992231677, G2293228691, G2387030025, G3307012285, G3681338154, G3693695517, G4578011331, G477710933, G4845925241, G5102071092, G532800669, G5361939448, G5401592639, G5452694287, G548651216, G5642993642, G5881163704, G5951298939, G6267554473, G6638163239, G7044287974, G7434853267, G7821943007, G7877839759, G8188694029, G829411124, G8354662170, G84477964, G8667838976, G8691980622, G8857994536
OpenAlex ID: W4417248165