Extrinsic upper bound of the eigenvalue for p-Laplacian. (July 2020)

• Record Type: Journal Article
• Authors: Chen, Hang
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 58C40 -- 53C42 -- 35P15; Reilly-type inequality -- p-Laplacian -- 1st eigenvalue -- Upper curvature bound; 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.2020.111833
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let M be an m -dimensional closed orientable submanifold in an n -dimensional Riemannian manifold N . When the sectional curvature of N is bounded above by δ, we obtain an upper bound for the first nonzero eigenvalue of the p -Laplacian in terms of the second fundamental form of M and δ . This generalizes the Reilly-type inequality for the Laplacian (Heintze, 1988; Reilly, 1977) to the p -Laplacian and extends the work of Chen and Wei (2019) and Du and Mao (2015) for the p -Laplacian.