拉梅方程和板理论的几何问题
Geometric Aspects of the Lame Equation and Plate Theory
摘要：
近年来，人们逐渐认识到德拉姆上同调理论与弹性理论中圣维南相容条件的密切关系。本文将讨论隐藏在拉梅方程和板块理论中的霍奇理论和德拉姆上同调理论。我们将证明Lame方程解的一个分解定理，然后利用这个分解定理提出一个修正的板理论，它与物理学的一般原理和Lame方程的数学结构相容。
英文摘要：
Over the past few years, it is gradually understood that de Rham Cohomology Theory is closely related to Saint-Venant's compatibility condition in the Elasticity Theory. In this article, we will discuss the Hodge Theory and de Rham Cohomology Theory hidden in the Lame Equation and in the Plate Theory. we will prove a Decomposition Theorem for the solutions of the Lame Equation, and then use this Decomposition Theorem to present a modified Plate Theory, which is compatible with the general principles of Physics and the mathematical structure of the Lame Equation.
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