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

Phillip S. Harrington; Andrew Raich

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arXiv · 1209.4044

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

Phillip S. Harrington·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.

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Phillip S. Harrington, Andrew Raich. 2012-09-18. Sobolev Spaces and Elliptic Theory on Unbounded Domains in $\mathbb R^n$. https://arxiv.org/abs/1209.4044

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