On the Dirichlet problem for general augmented Hessian equations

In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampère and k-Hes...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 269; no. 6; pp. 5204 - 5227
Main Authors Jiang, Feida, Trudinger, Neil S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.09.2020
Subjects
Augmented Hessian equations
Dirichlet problem
Regular matrix
Second derivative estimates
Dirichlet problem
Augmented Hessian equations
Second derivative estimates
Regular matrix
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Summary:In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampère and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.04.004