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arXiv · 2512.15277

Carleson-type removability for $p$-parabolic equations

Michał Borowski·Theo Elenius·Leah Schätzler·David Stolnicki
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Abstract

We characterize removable sets for H\"older continuous solutions to degenerate parabolic equations of $p$-growth. A sufficient and necessary condition for a set to be removable is given in terms of an intrinsic parabolic Hausdorff measure, which depends on the considered H\"older exponent. We present a new method to prove the sufficient condition, which relies only on fundamental properties of the obstacle problem and supersolutions, and applies to a general class of operators. For the necessity of the condition, we establish the H\"older continuity of solutions with measure data, provided the measure satisfies a suitable decay property. The techniques developed in this article provide a new point of view even in the case $p=2$.

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Michał Borowski, Theo Elenius, Leah Schätzler, David Stolnicki. 2025-12-17. Carleson-type removability for $p$-parabolic equations. https://arxiv.org/abs/2512.15277

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