Geodesic
Restrictions of Sobolev W_p^1(R^2)-spaces to planar rectifiable curves
Alexander I. Tyulenev1
1Steklov Mathematical Institute of Russian Academy of Sciences
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 507-531

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We construct explicit examples of Frostman-type measures concentrated on arbitrary simple rectifiable curves $\Gamma\subset\mathbb{R}^{2}$ of positive length. Based on such constructions we obtain for each $p \in (1,\infty)$ an exact description of the trace space $W^{1}_{p}(\mathbb{R}^{2})|_{\Gamma}$ of the first-order Sobolev space $W^{1}_{p}(\mathbb{R}^{2})$ to an arbitrary simple rectifiable curve $\Gamma$ of positive length.  
DOI : 10.54330/afm.115393
Keywords: Traces, extensions, Sobolev spaces, Frostman measures, measures on curves

Alexander I. Tyulenev  1

1 Steklov Mathematical Institute of Russian Academy of Sciences 
Alexander I. Tyulenev. Restrictions of Sobolev W_p^1(R^2)-spaces to planar rectifiable curves. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 507-531. doi: 10.54330/afm.115393
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