Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations. (March 2022)

• Record Type: Journal Article
• Authors: Li, You; Li, Mengni
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 35B65 -- 53A15 -- 35B51; Dirichlet problem -- Fully nonlinear equations -- Auxiliary functions; 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.2021.112681
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We are concerned in this paper with the boundary regularity of solutions to the Dirichlet problem for a class of fully nonlinear elliptic partial differential equations. Constructing delicate sub-solutions leads us to effective boundary regularity estimates of convex solutions to the problem. Emphasis here is on the relation of our boundary regularity result with the convexity of the domain described by an ( a, η ) type.