高频下振动的夹紧板类似于振动的膜
A Vibrating Clamped Plate Resembles a Vibrating Membrane at High Frequency
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中文总结 AI 辅助
本研究针对夹紧板特征值问题，证明其特征函数可由满足亥姆霍兹方程的振荡分量近似，误差随频率指数衰减，还建立了其边界局部化的上界，表明高频下夹紧板类似振动膜。
中文摘要 AI 辅助
我们研究夹紧板特征值问题，证明夹紧板特征函数可在L²意义上由其振荡分量（满足亥姆霍兹方程）近似，误差在任意紧子域上随频率指数快速衰减；此外，我们建立夹紧板特征函数边界局部化的上界，该上界与膜特征函数所观察到的类似。
英文摘要
We study the clamped plate eigenvalue problem. We show that clamped plate eigenfunctions can be approximated in the $L^2$-sense by their oscillatory components, which solve the Helmholtz equation, with an error that decays exponentially fast in the frequency on any compact subdomain. Additionally, we establish an upper bound on the boundary localization of clamped plate eigenfunctions analogous to the one observed for membrane eigenfunctions.
