四川理工学院学报（自然科学版）2018，Vol.31Issue(3)：81-85,5.DOI:10.11863/j.suse.2018.03.13
Laplace算子的特征函数系在三个空间中的完备性证明方法
Proof Method of the Completeness in 3 Spaces of the Eigenfunction System of Laplace Operator
摘要
Abstract
The existence of the eigenvalue and eigenfunction of the Laplace operator was obtained by means of calculus of variation in consideration of the nature of the laplace operator eigenvalue and eigenfunction under the Dirichlet boundary condition.Sequence of eigenvalues tending to infinity was applied to the proof of the orthogonal complete system nature of the eigenfunction system in H10(Ω)firstly.The denseness was applied to the proof of the orthonormal system nature of the eigen-function system in L2(Ω)secondly.Finally,the complete system nature of the eigenfunction system in H2(Ω)∩H10(Ω)was proved by the L2estimation of the linear elliptic partial differential equations of second order.This study provides more insight into the classical knowledge with strict and perfect proof.关键词
Laplace 算子/Dirichlet边界条件/特征值序列/特征函数系的完备性Key words
Laplace operator/Dirichlet boundary condition/sequence of eigenvalues/completeness of eigenfunction分类
数理科学引用本文复制引用
邢家省,杨义川..Laplace算子的特征函数系在三个空间中的完备性证明方法[J].四川理工学院学报（自然科学版）,2018,31(3):81-85,5.基金项目
国家自然科学基金资助项目(11771004) （11771004）
北京航空航天大学校级重大教改项目(2016) （2016）
