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Abstract and Applied Analysis
Volume 2013, Article ID 650870, 7 pages
http://dx.doi.org/10.1155/2013/650870
Review Article

A Priori Bounds in and in for Solutions of Elliptic Equations

Dipartimento di Matematica, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 21 March 2013; Accepted 15 May 2013

Academic Editor: Rodrigo Lopez Pouso

Copyright © 2013 Sara Monsurrò and Maria Transirico. 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

We give an overview on some recent results concerning the study of the Dirichlet problem for second-order linear elliptic partial differential equations in divergence form and with discontinuous coefficients, in unbounded domains. The main theorem consists in an -a priori bound, . Some applications of this bound in the framework of non-variational problems, in a weighted and a non-weighted case, are also given.