Reilly-type inequalities for p-Laplacian on submanifolds in space forms. (July 2019)

• Record Type: Journal Article
• Authors: Chen, Hang; Wei, Guofang
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 210
• Page End: 217
• Publication Date: 2019-07
• Subjects: 58C40 -- 53C42 -- 35P15; Reilly-type inequality -- p-Laplacian -- Eigenvalue estimate -- Submanifolds; 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.2019.02.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let M be an n -dimensional closed orientable submanifold in an N -dimensional space form. When 1 < p ≤ n 2 + 1, we obtain an upper bound for the first nonzero eigenvalue of the p -Laplacian in terms of the mean curvature of M and the curvature of the space form. This generalizes the Reilly inequality for the Laplacian (Soufi and Ilias, 1992; Reilly, 1977) to the p -Laplacian and extends the work of Du and Mao (2015) for the p -Laplacian.