| 郭 希,魏念念,向 妮,潘 岑.黎曼流形上具有Neumann边界条件的Monge-Amp`ere型方程[J].数学年刊A辑,2020,41(3):283~298 |
| 黎曼流形上具有Neumann边界条件的Monge-Amp`ere型方程 |
| Monge-Amp`ere Type Equations with Neumann Boundary Conditions on Riemannian Manifolds |
| Received:December 10, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0020 |
| 中文关键词: 二阶导数估计, Monge-Amp`ere 型方程, Neumann 问题, 黎曼流形 |
| 英文关键词:Second derivative estimate, Monge-Amp`ere type equation, Neumann problem, Riemannian manifold |
| 基金项目:国家自然科学基金(No.,11971157, No.,11501184)和湖北省教育厅重点项目(No.,D20171004) |
| Author Name | Affiliation | | GUO Xi | Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062, China. | | WEI Niannian | Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062, China. | | XIANG Ni | Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062, China. | | PAN Cen | Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062, China. |
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| 中文摘要: |
| 文章研究了黎曼流形上具有Neumann边界条件的Monge-Amp`ere型方程的全局正则性,并将其在欧几里得空间中的主要结论推广到了曲面空间. |
| 英文摘要: |
| In this paper, the authors consider the global regularity for Monge-Amp`ere type equations with the Neumann boundary conditions on Riemannian manifolds, and extend the main conclusions in the Euclidean flat space to curved spaces. |
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