Directional ellipticity on special domains: Weak Maximum and Phragmén–Lindelöf principles. (July 2019)

• Record Type: Journal Article
• Authors: Capuzzo Dolcetta, Italo; Vitolo, Antonio
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 69
• Page End: 82
• Publication Date: 2019-07
• Subjects: 35J60 -- 35B50 -- 35B53 -- 35D40; Nonlinear elliptic operators -- Maximum principles -- Unbounded domains -- Phragmén–Lindelöf principles; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains Ω ⊂ R n of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along the bounded directions of Ω, with possible degeneracy along the unbounded directions.