Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains-Reference-Cited by-同舟云学术

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

Published:2008 Issue: Volume:2008 Page:1-19
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Amendola M. E.¹,Rossi L.²,Vitolo A.¹

Affiliation:

1. Dipartimento di Matematica e Informatica, Università di Salerno, P. Grahamstown, 84084 Fisciano (SA), Italy

2. Dipartimento 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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2008/178534.pdf

Reference32 articles.

1. Grundlehren der Mathematischen Wissenschaften,1983

2. User’s guide to viscosity solutions of second order partial differential equations

3. American Mathematical Society Colloquium Publications,1995

4. Encyclopedia of Mathematical Sciences 32,1991

Cited by 29 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence of bounded solutions of fully nonlinear elliptic equations modeling the first passage time in cylindrical domains;Differential and Integral Equations;2024-03-01

2. Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form;Nonlinear Analysis;2023-10

3. The Alexandroff–Bakelman–Pucci estimate via positive drift;Pure and Applied Analysis;2023-06-26

4. Aleksandrov-Bakelman-Pucci maximum principle for L-viscosity solutions of equations with unbounded terms;Journal de Mathématiques Pures et Appliquées;2022-12

5. Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues;Advances in Nonlinear Analysis;2022-01-01