| 一类边值问题 |
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| 引用本文： | 涂天亮,朱登军. 一类边值问题[J]. 华北水利水电学院学报, 2008, 29(4) |
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| 作者姓名： | 涂天亮 朱登军 |
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| 作者单位： | 华北水利水电学院,河南,郑州,450011;河南省人民医院,河南,郑州,450003 |
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| 摘 要： | 设D是可求长Jordan闭曲线围成的单连域,g1(x,y)和g2(x,y)是D=Γ上的连续函数,证明了在D内调和且其连续偏导数可延拓到D=Γ上的调和函数存在的充要条件,讨论了这类边值问题解的惟一性,并得到了解的线积分表达式.
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| 关 键 词： | 边值问题 调和函数 存在性 惟一性 线积分表示 |
A Class of Boundary Value Problem |
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| TU Tian-liang,ZHU Deng-jun. A Class of Boundary Value Problem[J]. Journal of North China Institute of Water Conservancy and Hydroelectric Power, 2008, 29(4) |
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| Authors: | TU Tian-liang ZHU Deng-jun |
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| Abstract: | Let D be a simply connected domain bounded by a closed Jordan Curve Γ.Suppose g1(x,y) and g2(x,y) are continuous functions on Γ.The necessary and sufficient conditions for existence of u(x,y) are proved,which is harmonic in D and its continuous partial derivatives extending to D∈Γ.The uniqueness of solution to the boundary value problem is discussed,and the representation of the solution is obtained. |
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| Keywords: | boundary value problem harmonic function existence uniqueness representation |
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