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

math.AP

/ Authors

/ Abstract

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.

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

math.AP

/ Authors

Phillip S. Harrington, Andrew Raich

/ Abstract

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.