| 李文略.各向异性电介质静电场泊松方程的变分问题[J].海南师范大学学报自科版,2022,35(2):194-199 |
| 各向异性电介质静电场泊松方程的变分问题 |
| Variational Problem of Poisson Equation in Electrostatic Field ofAnisotropic Dielectric |
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| DOI：10.12051/j.issn.1674-4942.2022.02.015 |
| 中文关键词: 各向异性电介质 泊松方程 对称正定算子 变分问题 能量密度泛函 |
| 英文关键词: anisotropic dielectric Poisson equation symmetric positive operator variational problem energy density
functional |
| 基金项目: |
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| 摘要点击次数: 467 |
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| 中文摘要: |
| 根据对称正定算子方程的变分原理，将各向异性电介质静电场泊松方程第一和第二边
值问题转化为与之等价的变分问题。发现泊松方程实质上是与之等价的变分问题中所构造泛函
取得极值时所满足的奥斯特罗格拉茨基方程。由泛函的核函数定义了各向异性电介质静电场的
能量密度，并由该概念出发推导出能量密度泛函。富有物理意义的是各向异性电介质静电场的泊
松方程是能量密度泛函取得极值的必要条件，泊松方程的电势解是能量密度泛函取得极值的极值
函数。 |
| 英文摘要: |
| The first and the second boundary value problem for Poisson equation in electrostatic of anisotropic dielectric
was transformed into an equivalent variational problem, according to the variational principle of symmetric positive operator
equation. It is founded that Poisson equation is essentially the Ostrongradski equation that is satisfied when the extremum
of the functional constructed for the equivalent variational problem is obtained. The energy density in electrostatic of aniso⁃
tropic dielectric is defined by kernel function of the functional in the variational problem, and then the energy density func⁃
tional is derived from the concept. It has great physical signification that the Poisson equation in electrostatic of anisotropic
dielectric is the necessary condition for the energy density functional to obtain the extreme value and the potential solution
of Poisson equation is the extreme function of the energy density functional to obtain the extreme value. |
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