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arXiv · 2111.03381

Removability of product sets for Sobolev functions in the plane

Tapio Rajala·Ugo Bindini
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Abstract

We study conditions on closed sets $C,F \subset \mathbb{R}$ making the product $C \times F$ removable or non-removable for $W^{1,p}$. The main results show that the Hausdorff-dimension of the smaller dimensional component $C$ determines a critical exponent above which the product is removable for some positive measure sets $F$, but below which the product is not removable for another collection of positive measure totally disconnected sets $F$. Moreover, if the set $C$ is Ahlfors-regular, the above removability holds for any totally disconnected $F$.

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Tapio Rajala, Ugo Bindini. 2021-11-05. Removability of product sets for Sobolev functions in the plane. https://arxiv.org/abs/2111.03381

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