Restrictions of Sobolev $W_{p}^{1}(\mathbb{R}^{2})$-spaces to planar rectifiable curves

Alexander Tyulenev

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arXiv · 2010.05286

Restrictions of Sobolev $W_{p}^{1}(\mathbb{R}^{2})$-spaces to planar rectifiable curves

Alexander Tyulenev

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Abstract

We construct explicit examples of Frostman-type measures concentrated on arbitrary planar rectifiable curves of positive length. Based on such constructions we obtain for each $p \in (1,\infty)$ an exact description of the trace space of the first-order Sobolev space $W^{1}_{p}(\mathbb{R}^{2})$ to an arbitrary planar rectifiable curve $\Gamma \subset \mathbb{R}^{2}$ of positive length.

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BibTeX RIS

Alexander Tyulenev. 2020-10-11. Restrictions of Sobolev $W_{p}^{1}(\mathbb{R}^{2})$-spaces to planar rectifiable curves. https://arxiv.org/abs/2010.05286

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