International Journal of Differential Equations
Volume 2011 (2011), Article ID 572824, 17 pages
Research Article

𝑊 𝟐 , 𝟐 A Priori Bounds for a Class of Elliptic Operators

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

Received 17 June 2011; Accepted 5 August 2011

Academic Editor: Charles E. Chidume

Copyright © 2011 Sara Monsurrò et al. 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.


We obtain some 𝑊 2 , 2 a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.