Interior and boundary gradient estimates for solutions to Hessian equations satisfying Neumann boundary conditions. (June 2020)

• Record Type: Journal Article
• Authors: Dong, Weisong
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35B45 -- 35J66; Gradient estimate -- Neumann problem -- Fully nonlinear Hessian equations -- 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.2019.111733
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the a priori gradient estimate for admissible solutions to the Neumann problem of fully nonlinear Hessian equations on Riemannian manifolds. We derive the interior gradient estimate for admissible solutions, and then we establish the boundary gradient estimate by reducing it to the interior gradient estimate.