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arXiv · 2610.35780

The generic structure of the singular set in the Stefan problem

Giacomo Colombo·Alessio Figalli
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Abstract

We show that, in every space dimension $n\ge2$, 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, $\dim_{\mathrm{par}}(Σ)\le n-2$. 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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Giacomo Colombo, Alessio Figalli. 2026-10-26. The generic structure of the singular set in the Stefan problem. https://arxiv.org/abs/2610.35780

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