Gradient estimates for Neumann boundary value problem of Monge-Ampère type equations on Riemannian manifolds. (February 2017)

• Record Type: Journal Article
• Authors: Guo, Xi; Xiang, Ni
• Is Part Of: Nonlinear analysis. Volume 150(2017)
• Page Start: 151
• Page End: 158
• Publication Date: 2017-02
• Subjects: Gradient estimates -- Monge-Ampère type equations -- Neumann problem -- Riemannian manifolds; 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.2016.11.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the Monge-Ampère type equations with the Neumann boundary conditions on Riemannian manifolds. Our main result is the gradient estimates for the degenerate elliptic solution, which is the extension of the main theorem in Jiang et al. (2016) from R n to Riemannian manifolds.