| 退化秩为0的二阶椭圆型方程的边值问题 |
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| 引用本文： | 闻国椿. 退化秩为0的二阶椭圆型方程的边值问题[J]. 烟台大学学报(自然科学与工程版), 2004, 17(1): 1-8 |
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| 作者姓名： | 闻国椿 |
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| 作者单位： | 北京大学,数学学院,北京,100871 |
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| 摘 要： | 许多作者提出和讨论了二阶退化椭圆型方程的一些边值问题，如Dirichlet边值问题和混合边值问题。本文讨论高维区域中退化秩为0的二阶椭圆型方程的一些边值问题，这些问题包括上述问题作为特殊情况．先给出这些问题的提法。然后使用列紧性原理和极值原理证明了上述二阶椭圆型方程边值解的存在性和唯一性。
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| 关 键 词： | 退化椭圆型方程 边值问题 退化秩 列紧性原理 极值原理 |
Boundary Value Problems for Second Order Elliptic Equations with Degenerate Rank 0 |
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| Abstract. Boundary Value Problems for Second Order Elliptic Equations with Degenerate Rank 0[J]. Journal of Yantai University(Natural Science and Engineering edirion), 2004, 17(1): 1-8 |
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| Authors: | Abstract |
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| Abstract: | Many authors posed and discussed some boundary value problems,mainly the Dirichlet problem and mixed boundary value problem for second order elliptic equations with parabolic degeneracy.In this paper some boundary value problems for the degenerate elliptic equations of second order are discussed in a high dimensional domain,which include the above problems as a special case.Fristly the boundary value problems for the equations is formulated,and then by using the compactness principle, the existence of solutions for the above problems is proved. |
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| Keywords: | boundary value problems degeneracte elliptic equations existance and uniqueness of solutions |
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