论文标题
sobolev $ w_ {p}^{1}的限制
Restrictions of Sobolev $W_{p}^{1}(\mathbb{R}^{2})$-spaces to planar rectifiable curves
论文作者
论文摘要
我们构建了霜冻型测度的明确例子，该措施集中在任意平面可整流曲线上的正长度。基于此类构造，我们为（1，\ infty）中的每个$ p \获得了一阶Sobolev空间的痕迹空间$ w^{1} _ {p}（\ Mathbb {r}^{2} $）的准确描述
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 $Γ\subset \mathbb{R}^{2}$ of positive length.
