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arXiv · 2603.06352

Dimension of the singular set in the parabolic obstacle problem

Alejandro Martínez·Xavier Ros-Oton
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Abstract

In this paper we study the singular set in the parabolic obstacle problem for general obstacles $\varphi \in C^{2,1}$. We prove that the singular set has parabolic Hausdorff dimension at most $n-1$. Prior to our result, this was only known when $\Delta \varphi \equiv -1$. Our approach combines a truncated parabolic frequency formula and monotonicity estimates with an iterative argument showing that the frequency is saturated for all values of the truncation parameter between $2$ and $3$.

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Alejandro Martínez, Xavier Ros-Oton. 2026-03-06. Dimension of the singular set in the parabolic obstacle problem. https://arxiv.org/abs/2603.06352

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