The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains

We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity o...

Full description

Saved in:
Bibliographic Details
Published in:Communications in partial differential equations 2005-11, Vol.30 (12), p.1863-1881
Main Authors: Capuzzo-Dolcetta, I., Leoni, F., Vitolo, A.
Format: Article
Language:English
Subjects:
Fully nonlinear elliptic equations
Maximum Principle
Unbounded domains
Viscosity solutions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605300500300030