On the growth of supersolutions of nonlinear PDE's on exterior domains. (November 2016)

• Record Type: Journal Article
• Authors: Impera, Debora; Pigola, Stefano
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 20
• Page End: 31
• Publication Date: 2016-11
• Subjects: 35J60 -- 53C42 -- 53C21; Nonlinear elliptic operators -- Growth estimate -- Exterior graphs -- Mean curvature; 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.2016.08.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain a comparison principle on annuli, with "catenoid-like" functions, for supersolutions of non-linear elliptic PDEs over exterior domains in a non-positively curved manifold with a pole. This result is applied to get an upper estimate on the growth of such supersolutions and, in particular, of exterior graphs of non-negative mean curvature.