Sobolev Spaces and Elliptic Theory on Unbounded Domains in ${\mathbb{R}}^n$

In this article, we develop the theory of weighted $L^2$ Sobolev spaces on unbounded domains in ${\mathbb{R}}^n$. As an application, we establish the elliptic theory for elliptic operators and prove trace and extension results analogous to the bounded, unweighted case.