Sobolev spaces and elliptic theory on unbounded domains in $\mathbb{R}^n$
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.