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arXiv · 2412.18402

Removable singularities for Lipschitz fractional caloric functions in time varying domains

Joan Hernández
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Abstract

In this paper we study removable singularities for regular $(1,\frac{1}{2s})$-Lipschitz solutions of the $s$-fractional heat equation for $1/2<s<1$. To do so, we define a Lipschitz fractional caloric capacity and study its critical dimension and the $L^2$-boundedness of a pair of singular integral operators, whose kernels will be the gradient of the fundamental solution of the fractional heat equation and its conjugate.

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Joan Hernández. 2024-12-24. Removable singularities for Lipschitz fractional caloric functions in time varying domains. https://arxiv.org/abs/2412.18402

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