论文标题
riemannian歧管上线性弹性中的两项光谱渐近学
Two-term spectral asymptotics in linear elasticity on a Riemannian manifold
论文作者
论文摘要
在本说明中，通过解释\ cite {liu-21}中采用的两种关键方法，并通过给出一些言论，我们表明定理1.1在\ cite {liu-21}中的证明是基于强烈连续的半群和伪差异操作员的严格证明。由Matteo Capoferri，Leonid Friedlander，Michael Levitin和Dmitri Vassiliev在\ cite {cafrleva-22}中给出的所有评论\ cite \ cite {liu-21}，这是不正确的。 \ cite {cafrleva-22}中所谓的“数值反例”是弹性特征值计数函数的两项渐近学的无用示例。显然，结论和\ cite {liu-21}的证明是完全正确的。
In this note, by explaining two key methods that were employed in \cite{Liu-21} and by giving some remarks, we show that the proof of Theorem 1.1 in \cite{Liu-21} is a rigorous proof based on theory of strongly continuous semigroups and pseudodifferential operators. All remarks and comments to paper \cite{Liu-21}, which were given by Matteo Capoferri, Leonid Friedlander, Michael Levitin and Dmitri Vassiliev in \cite{CaFrLeVa-22}, are incorrect. The so-called "numerical counter-examples" in \cite{CaFrLeVa-22} are useless examples for the two-term asymptotics of the counting functions of the elastic eigenvalues. Clearly, the conclusion and the proof of \cite{Liu-21} are completely correct.
