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arXiv · 1706.07687

A removability theorem for Sobolev functions and detour sets

Dimitrios Ntalampekos
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Abstract

We study the removability of compact sets for continuous Sobolev functions. In particular, we focus on sets with infinitely many complementary components, called "detour sets", which resemble the Sierpiński gasket. The main theorem is that if $K\subset \mathbb R^n$ is a detour set and its complementary components are sufficiently regular, then $K$ is $W^{1,p}$-removable for $p>n$. Several examples and constructions of sets where the theorem applies are given, including the Sierpiński gasket, Apollonian gaskets, and Julia sets.

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BibTeXRIS

Dimitrios Ntalampekos. 2019-06-26. A removability theorem for Sobolev functions and detour sets. https://doi.org/10.1007/s00209-019-02405-7

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