Abstract and Applied Analysis
Volume 2008 (2008), Article ID 178534, 19 pages
doi:10.1155/2008/178534
Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains
M.E. Amendola1
, L. Rossi2
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
Abstract
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.