| 吴亚东,李合朋.一类Monge-Amp\`{e}re 方程解的二阶导数估计[J].数学研究及应用,2014,34(4):475~480 |
| 一类Monge-Amp\`{e}re 方程解的二阶导数估计 |
| Second Order Derivative Estimates of the Solutions of a Class of Monge-Amp\`{e}re Equations |
| 投稿时间：2013-07-19 修订日期：2014-01-14 |
| DOI：10.3770/j.issn:2095-2651.2014.04.010 |
| 中文关键词: Monge-Amp\`{e}re 方程 导数估计 相对微分几何. |
| 英文关键词:Monge-Amp\`{e}re equation derivative estimate relative differential geometry. |
| 基金项目:国家自然科学基金(Grant Nos.11301231; 11171235). |
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| 中文摘要: |
| 本文考虑了相对微分几何中的一类Monge-Amp\`{e}re 方程.当给定光滑严格凸区域和零边值条件时, 我们得到了此类方程凸解的二阶导数估计. |
| 英文摘要: |
| In this paper, we consider a class of Monge-Amp\`{e}re equations in relative differential geometry. Given these equations with zero boundary values in a smooth strictly convex bounded domain, we obtain second order derivative estimates of the convex solutions. |
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