Abstract and Applied Analysis

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

M. E. Amendola, L. Rossi, and A. Vitolo

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 178534, 19 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969165

Digital Object Identifier
doi:10.1155/2008/178534

Mathematical Reviews number (MathSciNet)
MR2407278

Zentralblatt MATH identifier
1187.35065

Citation

Amendola, M. E.; Rossi, L.; Vitolo, A. Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains. Abstr. Appl. Anal. 2008 (2008), Article ID 178534, 19 pages. doi:10.1155/2008/178534. https://projecteuclid.org/euclid.aaa/1220969165


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