Oblique boundary value problems for n-1type augmented Hessian equations
Abstract
In this paper, we study the global regularity of oblique boundary value problems for n-1 type augmented Hessian equations on a bounded domain, without imposing any convexity condition either on the domain or on the matrix-valued function in the n-1 type augmented Hessian equations. We establish a global existence and uniqueness theory for classical elliptic solutions by deriving global a priori estimates up to second-order derivatives. Besides the known applications for n-1 type Monge-Ampere operators in optimal transportation and geometric optics, the general theory here embraces equations raised by Li-Sheng, Some Dirichlet problems arising from conformal geometry. Pac. J. Math. 251, 2011, 337-359 and Guan-Qiu-Yuan, Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms. Adv. Math. 343, 2019, 538-566.
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BibTeX
@misc{hu2026oblique,
title = {{Oblique boundary value problems for n-1type augmented Hessian equations}},
author = {Zhibo Hu and Feida Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11400},
eprint = {2610.11400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11400},
}
RIS
TY - UNPB
TI - Oblique boundary value problems for n-1type augmented Hessian equations
AU - Zhibo Hu
AU - Feida Jiang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.11400
UR - https://arxiv.org/abs/2610.11400
AB - In this paper, we study the global regularity of oblique boundary value problems for n-1 type augmented Hessian equations on a bounded domain, without imposing any convexity condition either on the domain or on the matrix-valued function in the n-1 type augmented Hessian equations. We establish a global existence and uniqueness theory for classical elliptic solutions by deriving global a priori estimates up to second-order derivatives. Besides the known applications for n-1 type Monge-Ampere operators in optimal transportation and geometric optics, the general theory here embraces equations raised by Li-Sheng, Some Dirichlet problems arising from conformal geometry. Pac. J. Math. 251, 2011, 337-359 and Guan-Qiu-Yuan, Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms. Adv. Math. 343, 2019, 538-566.
ER -