PreprintCC BY-NC-SA 4.0arXiv
The generic structure of the singular set in the Stefan problem
Abstract
We show that, in every space dimension n≥2, the singular set Σ of a generic (in the Baire-category sense) solution of the Stefan problem is countably parabolically (n−2)-rectifiable. In particular, dimpar(Σ)≤ n−2. This is achieved by proving the following sharp result: in every space dimension, points of the maximal stratum of a generic solution are discrete in space-time.
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BibTeX
@misc{colombo2026generic,
title = {{The generic structure of the singular set in the Stefan problem}},
author = {Giacomo Colombo and Alessio Figalli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35780},
eprint = {2610.35780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35780},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The generic structure of the singular set in the Stefan problem
AU - Giacomo Colombo
AU - Alessio Figalli
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35780
UR - https://arxiv.org/abs/2610.35780
AB - We show that, in every space dimension n≥2, the singular set Σ of a generic (in the Baire-category sense) solution of the Stefan problem is countably parabolically (n−2)-rectifiable. In particular, dim_par(Σ)≤ n−2. This is achieved by proving the following sharp result: in every space dimension, points of the maximal stratum of a generic solution are discrete in space-time.
ER -