Advances in Differential Equations

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

Phillip S. Harrington and Andrew Raich

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1399395722

Mathematical Reviews number (MathSciNet)
MR3252898

Zentralblatt MATH identifier
1301.46015

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 35J15: Second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 46B70: Interpolation between normed linear spaces [See also 46M35]

Citation

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.


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