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| 摘要: |
| 本文研究了一类抛物型Monge-Ampère型方程的Cauchy-Neumann问题.通过构造辅助函数，利用函数在极大值点的性质及柯西不等式等方法对方程的解进行估计，得到了方程解的全局二阶梯度估计.接着利用抛物方程的一般理论，进一步得到在光滑条件下，解的长时间存在性，推广了抛物型Monge-Ampère方程的结果. |
| 关键词: 抛物型Monge-Ampère型方程 Cauchy-Neumann问题 先验估计 梯度估计 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:湖北省教育厅科学技术研究计划重点项目（D20171004）. |
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| THE CAUCHY-NEUMANN PROBLEM FOR PARABOLIC TYPE AND MONGE-AMPÈRE TYPE EQUATIONS |
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XIANG Ni,WU Yan,DOU Nan,ZHANG Jun-wei
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| Abstract: |
| In this paper, we study the Cauchy-Neumann problem for parabolic type and Monge-Ampère type equations. By establishing an anxiliary function, using the methods of the properity at the maximum point and cauchy inequality, we prove the global gradient estimates for second order derivatives. And by using the general theory of parabolic equations, we obtain that such solution exists for all times under smoothness and regularity conditions, which generalizes the results of parabolic type and Monge-Ampère type equations. |
| Key words: parabolic type and Monge-Ampère type equation Cauchy-Neumann problem a priori estimate gradient estimate |
