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

Phillip S. Harrington; Andrew Raich

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

Analysis of PDEs 2014-06-26 v1 Functional Analysis

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.

Keywords

Sobolev spaces elliptic theory unbounded domains weighted $L^2$ spaces trace theorems extension theorems elliptic operators

Cite

@article{arxiv.1209.4044,
  title  = {Sobolev Spaces and Elliptic Theory on Unbounded Domains in $\mathbb R^n$},
  author = {Phillip S. Harrington and Andrew Raich},
  journal= {arXiv preprint arXiv:1209.4044},
  year   = {2014}
}

Comments

47 pages

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