Restrictions of Sobolev W_p^1(R^2)-spaces to planar rectifiable curves - Tyulenev, Alexander I. (Annales Fennici Mathematici, 2022)
We construct explicit examples of Frostman-type measures concentrated on arbitrary simple rectifiable curves \(ΓR^2\) of positive length. Based on such constructions we obtain for each \(p (1,∞)\) an exact description of the trace space \(W^1_p(R^2)|_Γ\) of the first-order Sobolev space \(W^1_p(R^2)\) to an arbitrary simple rectifiable curve \(Γ\) of positive length.