| 2n阶椭圆型复方程的Dirichlet边值问题 |
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| 引用本文： | 闻国椿,康世祥,柳企丰.2n阶椭圆型复方程的Dirichlet边值问题[J].四川师范大学学报(自然科学版),1990(3). |
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| 作者姓名： | 闻国椿 康世祥 柳企丰 |
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| 作者单位： | 北京大学，四川师范大学，四川师范大学 |
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| 摘 要： | 本文先使用解的先验估计和 Leray-Schauder 定理讨论了2u 阶非线性椭圆型复方程在单位圆上Dirichlet 边值问题的可解性.其次,使用积分方程的 Fredholm 定理讨论2u 阶线性椭圆型复方程上述边位问题的可解性.最后,我们还简略地讨论了两个未知实函敬的2n 阶线性与非线性椭圆型方程组的相应边值问题,在处理以上各边值问题时,都利用.关于方程 U_(?)=F(z)的 Dirichlet 边值问题解的积分表示式.
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| 关 键 词： | 2_n 阶椭圆型复方程 Dirichlet 边值问题 Leray-Schauder 定理 |
THE DIRICHLET BOUNDARY VALUE PROBLEMS FOR THE 2n ORDER ELLIPTIC COMPLEX EQUATIONS |
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| Wen Guochun.THE DIRICHLET BOUNDARY VALUE PROBLEMS FOR THE 2n ORDER ELLIPTIC COMPLEX EQUATIONS[J].Journal of Sichuan Normal University(Natural Science),1990(3). |
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| Authors: | Wen Guochun |
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| Institution: | Wen Guochun (Peking University)
Kang Shixiang Liu Qifeng(Sich Normal University) |
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| Abstract: | The objective of this paper is,at first using apriori estimates of solution and Leray-Schauder theorem,to discuss
Dirichlet boundary value problems on the unit disk for 2n order nonlinear elliptic complex equation is solvable,and using
Fredholm theorem of integral equation,to proved Linear elliptic complex equation is solvable,lastly to discuss briefly the
boundary value problems of the elliptic equations with 2 unknow real function in the case of 2n order linear and nonlin-
ear elliptic system.
To solve the above boundary value problems I.N.Vekua's integral forms about the Dirichlet boundary value prob-
lems of the equation u(?)=F(z)are used. |
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| Keywords: | 2n order elliptic complex equation Dirichlet boundary value problem Leray-Schauder theorem |
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