Remarks on paper "Two-term spectral asymptotics in linear elasticity''

Abstract

In this note, we shall point out that all ``numerically calculations'' and figures in \cite{CaFrLeVa-23} are wrong because these calculations are based on some incorrect formulas. Furthermore, by pointing out several serious errors in \cite{CaFrLeVa-23} and especially by Section 7, Proposition 7.1, Remarks 7.2--7.3, and Section 8 (a result of A. Pierzchalski and B. Ørsted) we show that the conclusions published by Matteo Capoferri, Leonid Friedlander, Michael Levitin and Dmitri Vassiliev (J Geom Anal (2023)33:242) as well as the main ``algorithm'' theory of the book \cite{SaVa-97} are completely wrong. Finally, we explain the correctness of proof of Theorem 1.1 in our paper \cite{Liu-21} by giving some remarks and putting the whole proof in Appendix (see also \cite{Liu-22b} and \cite{Liu-22c}).

39 pages, Latex; typos corrected, Section 7 is further explained, Section 8 and references added, and Proof of Theorem 1.1 is further explained (in Appendix)