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

#### 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.

#### Article information

Source
Adv. Differential Equations Volume 19, Number 7/8 (2014), 635-692.

Dates
First available in Project Euclid: 6 May 2014

Harrington, Phillip S.; Raich, Andrew. Sobolev spaces and elliptic theory on unbounded domains in $\mathbb{R}^n$. Adv. Differential Equations 19 (2014), no. 7/8, 635--692.https://projecteuclid.org/euclid.ade/1399395722