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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2018-05-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s13373-018-0124-2 |
| Summary: | 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. |
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| ISSN: | 1664-3607 1664-3615 |