| 一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题 |
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| 引用本文： | 王娟,刘辉昭.一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题[J].山东大学学报(理学版),2010,45(6):70-73. |
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| 作者姓名： | 王娟 刘辉昭 |
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| 作者单位： | 王娟,WANG Juan(内蒙古科技大学数理与生物工程学院,内蒙古包头,014010);刘辉昭,LIU Hui-zhao(河北工业大学理学院,天津,300130) |
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| 摘 要： | 证明了一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题的古典解的存在惟一性。用比较原理证明了该问题至多存在一个古典解。在一定条件下,通过构造辅助函数和闸函数,得到严格凸解的先验估计结果,进而利用连续性方法得到了该问题严格凸解的存在性。
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| 关 键 词： | Monge-Ampère方程 Neumann边界条件 先验估计 |
| 收稿时间： | 2009-08-18 |
The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equations |
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| WANG Juan,LIU Hui-zhao.The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equations[J].Journal of Shandong University,2010,45(6):70-73. |
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| Authors: | WANG Juan LIU Hui-zhao |
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| Institution: | 1. School of Mathematics,Physics and Biological Engineering,Inner Mongolia University of Science and Technology,
Baotou 014010, Inner Mongolia,China; 2. School of Sciences, Hebei University of Technology,
Tianjin 300130, China |
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| Abstract: | It is proved that a classical solution to the initial and Neumann boundary value problem for parabolic-type Monge-Ampère equation is existent and unique. Using compare principle, it is shown the uniqueness of the classical solution. By employing proper auxiliary functions and barrier functions, the priori estimations are obtained. The existence of the strict convex classical solution is obtained by the continuous method. |
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| Keywords: | Monge-Ampère equation Neumann boundary condition priori estimation |
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