各向异性电介质静电场拉普拉斯方程和能量密度泛函  

Laplace Equation and Energy Density Function in Electrostatic Field of Anisotropic Dielectric

作　　者：李文略 LI Wenue(College of Basic Education,Lingnan Normal University,Zhanjiang 524037,China)

机构地区：[1]岭南师范学院基础教育学院,广东湛江524037

出　　处：《河南财政金融学院学报（自然科学版）》2024年第1期12-17,共6页Journal of Henan Finance University(Natural Science Edition)

摘　　要：由各向异性电介质静电场的能量密度写出以电势为函数的能量密度泛函。拉普拉斯方程即为奥氏方程,是能量密度泛函取得极值的必要条件。拉普拉斯方程是算子方程,应用对称正定算子方程的变分原理构造与之相对应的泛函,从而由泛函的核函数引申出能量密度的概念。应用变分原理,将各向异性电介质静电场拉普拉斯方程的定解问题转换为与之相对应的变分问题。The energy density functional with the electric potential as a function is written by the energy density of electrostatic field in anisotropic dielectric.The Laplace equation is the Ostrogradski equation,which is the necessary condition for obtaining the extreme value of the energy destiny function.Laplace equation’s corresponding function is constructed by applying the variational principle of symmetric positive definite operator equation,and the concept of energy density is derived from the kernel function,because Laplace equation is an operator equation.By apply-ing the variational principle,the explicit solution to Laplace equation of electrostatic field in anisotropic dielectric is transformed into the corresponding variational problem.

关 键 词：各向异性电介质 拉普拉斯方程 能量密度泛函 算子方程 变分问题 

分 类 号：O441.4[理学—电磁学]