| Laplace 方程的球上 Dirichlet 问题解存在性的非标准证明 |
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| 引用本文： | 王建鹏. Laplace 方程的球上 Dirichlet 问题解存在性的非标准证明[J]. 高师理科学刊, 2011, 31(2): 36-39. DOI: 10.3969/j.issn.1007-9831.2011.02.011 |
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| 作者姓名： | 王建鹏 |
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| 作者单位： | 西北大学,数学系,陕西,西安,710127;河海大学常州校区,数理部,江苏,常州,213022 |
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| 摘 要： | Laplace方程具有广泛的物理背景,是一类基本的椭圆方程.引入曲面积分的非标准定义,直观地指出Green函数在调和与非调和点的差异,给出球上Dirichlet问题解存在性的非标准证明.
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| 关 键 词： | Laplace方程 Green函数 标准部分 单子 |
Non-standard proofs of the existence of solutions to the spherical Dirichlet problem for the Laplace differential equations |
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| WANG Jian-peng. Non-standard proofs of the existence of solutions to the spherical Dirichlet problem for the Laplace differential equations[J]. Journal of Science of Teachers＇College and University, 2011, 31(2): 36-39. DOI: 10.3969/j.issn.1007-9831.2011.02.011 |
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| Authors: | WANG Jian-peng |
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| Affiliation: | WANG Jian-peng1,2 |
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| Abstract: | Laplace equations are a kind of basic elliptic differential equations,which have been extensively applied in physics and technologies.The non-standard definition of surface integration was introduced,then the differences of Green function in harmonic and non-harmonic points was intuitively presented.Finally the explicit proofs for the existence of the solutions to the spherical Dirichlet problem was given using the non-standard analysis methods. |
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| Keywords: | Laplace equation Green function standard part monad |
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