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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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

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

First available in Project Euclid: 6 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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.

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