Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball

T. Sh. Kalmenov; B. D. Koshanov

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Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball

机译：球中多调和方程的Dirichlet问题的格林函数表示

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摘要

We explicitly construct the Green's function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Green’s function are of interest in their own right. In particular, the explicit representations for a solution to the Dirichlet problem for the biharmonic equation are important in elasticity.

机译：我们为任意维数空间中的球上的多调和方程的Dirichlet问题明确构造了格林函数。格林函数的公式本身很有趣。特别是，双调和方程Dirichlet问题解的显式表示对弹性很重要。

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来源
《Siberian Mathematical Journal》 |2008年第3期|共6页
作者
T. Sh. Kalmenov; B. D. Koshanov;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
polyharmonic equation; Dirichlet problem; Green's function;

机译：多调和方程;Dirichlet问题;格林函数;

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专利

1. Green Function Representation in the Dirichlet Problem for Polyharmonic Equations in a Ball [J] . T. Sh. Kalmenov, B. D. Koshanov, M. Yu. Nemchenko Doklady. Mathematics . 2008,第1期

机译：球中多调和方程的Dirichlet问题中的格林函数表示
2. Green function representation for the Dirichlet problem of the polyharmonic equation in a sphere [J] . T. Sh. Kalmenov, B. D. Koshanov, M. Y. Nemchenko Complex variables and elliptic equations . 2008,第2期

机译：球面中多调和方程Dirichlet问题的格林函数表示
3. On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation [J] . T. Sh. Kal’menov, D. Suragan Differential Equations . 2012,第3期

机译：关于构造多调和方程Dirichlet问题Green函数的新方法
4. On the representation of the Green function of the Dirichlet problem and their properties for the polyharmonic equations [C] . Bakytbek D. Koshanov, Maira D. Koshanova International Conference on Advancements in Mathematical Sciences . 2015

机译：关于Dirichlet问题的绿色功能的表示及其对多球方程的性质
5. Chip-firing games with Dirichlet eigenvalues and discrete Green's functions. [D] . Ellis, Robert Byron, III. 2002

机译：具有Dirichlet特征值和离散格林函数的筹码游戏。
6. Assumption of Boundary Values and the Greens Function in the Dirichlet Problem for the General Linear Elliptic Equation [O] . Felix E. Browder 1953

机译：一般线性椭圆型方程Dirichlet问题中的边值和格林函数的假设
7. ON REPRESENTATION OF GREEN’S FUNCTION OF THE DIRICHLET PROBLEM FOR BIHARMONIC EQUATION IN A BALL [O] . V.V. Karachik 2018

机译：在球中的比光arcononic方程中绿色函数的表示
8. Positivity for Equations Involving Polyharmonic Operators with Dirichlet BoundaryConditions [R] . Grunau, H. C., Sweers, G. 1995

机译：含Dirichlet边界条件的多调和算子方程的正定性

Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball

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