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


الملخص بالإنكليزية

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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