Oblique boundary value problems for augmented Hessian equations II. (May 2017)

• Record Type: Journal Article
• Authors: Jiang, Feida; Trudinger, Neil S.
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 148
• Page End: 173
• Publication Date: 2017-05
• Subjects: Oblique boundary value problem -- Augmented Hessian equations -- a priori; 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.2016.08.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we continue our investigations into the global theory of oblique boundary value problems for augmented Hessian equations. We construct a global barrier function in terms of an admissible function in a uniform way when the matrix function in the augmented Hessian is only assumed regular. This enables us to derive global second derivative estimates in terms of boundary estimates which are then obtained by strengthening the concavity or monotonicity conditions in our previous work on the strictly regular case. Finally we give some applications to existence theorems which embrace standard Hessian equations as special cases.