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Journal of Function Spaces and Applications
Volume 6, Issue 1, Pages 47-58
http://dx.doi.org/10.1155/2008/872891

The Dirichlet Problem for elliptic equations in unbounded domains of the plane

Dipartimento di Matematica e Informatica, Facoltà di Scienze MM.FF.NN., Università di Salerno, via Ponte Don Melillo, I 84084 Fisciano (SA), Italy

Received 1 February 2007

Academic Editor: Josip Pečarić

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of class VMO and satisfy a suitable condition at infinity.