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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