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. 
Phillip S. Harrington and Andrew Raich
math.AP math.FA