Sobolev extension in a simple case

Abstract

In this paper, we establish the existence of a bounded, linear extension operator $T:L^{2,p}(E)\to L^{2,p}({\mathbb{R}}^2)$ when $1<p<2$ and $E$ is a finite subset of ${\mathbb{R}}^2$ contained in a line.

19 pages, 3 figures