Abstract and Applied Analysis
Volume 2008 (2008), Article ID 178534, 19 pages
Research Article

Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains

M. E. Amendola,1 L. Rossi,2 and A. Vitolo1

1Dipartimento di Matematica e Informatica, Università di Salerno, P. Grahamstown, 84084 Fisciano (SA), Italy
2Dipartimento di Matematica, Università di Roma “La Sapienza”, P. le A. Moro 2, 00185 Roma, Italy

Received 17 July 2007; Revised 31 January 2008; Accepted 4 April 2008

Academic Editor: Y. Giga

Copyright © 2008 M. E. Amendola 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 are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.