Oblique boundary value problems for augmented Hessian equations I
Abstract In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the matrix function in the augmented Hessi...
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2018-05-01
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doaj-a956096aad014491b0a7d7fb2e41a3f42020-11-25T02:22:47ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152018-05-018235341110.1007/s13373-018-0124-2Oblique boundary value problems for augmented Hessian equations IFeida Jiang0Neil S. Trudinger1College of Mathematics and Statistics, Nanjing University of Information Science and TechnologyCentre for Mathematics and Its Applications, The Australian National UniversityAbstract In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the matrix function in the augmented Hessian, we develop a global theory for classical elliptic solutions by establishing global a priori derivative estimates up to second order. Besides the known applications for Monge–Ampère type operators in optimal transportation and geometric optics, the general theory here embraces Neumann problems arising from prescribed mean curvature problems in conformal geometry as well as general oblique boundary value problems for augmented k-Hessian, Hessian quotient equations and certain degenerate equations.http://link.springer.com/article/10.1007/s13373-018-0124-2Oblique boundary value problemsAugmented Hessian equationsSecond derivative estimatesGradient estimates |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Feida Jiang Neil S. Trudinger |
spellingShingle |
Feida Jiang Neil S. Trudinger Oblique boundary value problems for augmented Hessian equations I Bulletin of Mathematical Sciences Oblique boundary value problems Augmented Hessian equations Second derivative estimates Gradient estimates |
author_facet |
Feida Jiang Neil S. Trudinger |
author_sort |
Feida Jiang |
title |
Oblique boundary value problems for augmented Hessian equations I |
title_short |
Oblique boundary value problems for augmented Hessian equations I |
title_full |
Oblique boundary value problems for augmented Hessian equations I |
title_fullStr |
Oblique boundary value problems for augmented Hessian equations I |
title_full_unstemmed |
Oblique boundary value problems for augmented Hessian equations I |
title_sort |
oblique boundary value problems for augmented hessian equations i |
publisher |
World Scientific Publishing |
series |
Bulletin of Mathematical Sciences |
issn |
1664-3607 1664-3615 |
publishDate |
2018-05-01 |
description |
Abstract In this paper, we study global regularity for oblique boundary value problems of augmented Hessian equations for a class of general operators. By assuming a natural convexity condition of the domain together with appropriate convexity conditions on the matrix function in the augmented Hessian, we develop a global theory for classical elliptic solutions by establishing global a priori derivative estimates up to second order. Besides the known applications for Monge–Ampère type operators in optimal transportation and geometric optics, the general theory here embraces Neumann problems arising from prescribed mean curvature problems in conformal geometry as well as general oblique boundary value problems for augmented k-Hessian, Hessian quotient equations and certain degenerate equations. |
topic |
Oblique boundary value problems Augmented Hessian equations Second derivative estimates Gradient estimates |
url |
http://link.springer.com/article/10.1007/s13373-018-0124-2 |
work_keys_str_mv |
AT feidajiang obliqueboundaryvalueproblemsforaugmentedhessianequationsi AT neilstrudinger obliqueboundaryvalueproblemsforaugmentedhessianequationsi |
_version_ |
1724861708769427456 |