| 抛物型Monge-Ampère型方程的Cauchy-Neumann问题 |
| |
| 引用本文： | 向妮,吴燕,窦楠,张俊玮.抛物型Monge-Ampère型方程的Cauchy-Neumann问题[J].数学杂志,2017,37(6):1261-1274. |
| |
| 作者姓名： | 向妮 吴燕 窦楠 张俊玮 |
| |
| 作者单位： | 湖北大学数学与统计学学院, 湖北 武汉 430062,湖北大学数学与统计学学院, 湖北 武汉 430062,湖北大学数学与统计学学院, 湖北 武汉 430062,湖北大学数学与统计学学院, 湖北 武汉 430062 |
| |
| 基金项目： | 湖北省教育厅科学技术研究计划重点项目（D20171004）. |
| |
| 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 |
| 收稿时间： | 2017/1/13 0:00:00 |
| 修稿时间： | 2017/4/25 0:00:00 |
THE CAUCHY-NEUMANN PROBLEM FOR PARABOLIC TYPE AND MONGE-AMPÈRE TYPE EQUATIONS |
| |
| XIANG Ni,WU Yan,DOU Nan and ZHANG Jun-wei.THE CAUCHY-NEUMANN PROBLEM FOR PARABOLIC TYPE AND MONGE-AMPÈRE TYPE EQUATIONS[J].Journal of Mathematics,2017,37(6):1261-1274. |
| |
| Authors: | XIANG Ni WU Yan DOU Nan and ZHANG Jun-wei |
| |
| Institution: | School of Mathematics and Statistics, Hubei University, Wuhan 430062, China,School of Mathematics and Statistics, Hubei University, Wuhan 430062, China,School of Mathematics and Statistics, Hubei University, Wuhan 430062, China and School of Mathematics and Statistics, Hubei University, Wuhan 430062, China |
| |
| 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. |
| |
| Keywords: | parabolic type and Monge-Ampère type equation Cauchy-Neumann problem a priori estimate gradient estimate |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学杂志》浏览原始摘要信息 |
| 点击此处可从《数学杂志》下载免费的PDF全文 |
|
