Spectral asymptotics for linear elasticity with mixed boundary conditions
Analysis of PDEs
2024-02-13 v1 Differential Geometry
Spectral Theory
Abstract
In this note, we shall show that the two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions which were given by Capoferri and Mann in \cite{CaMa-24} essentially are old well-known results due to T. Branson, P. Gilkey, B. {\O}rsted and A. Pierzchalski in \cite{BGOP}. In addition, we further point out that the so-called ``general formulae'' in \cite{SaVa-97, CaFrLeVa-23} and the calculations for several examples in \cite{CaMa-24, CaFrLeVa-23} are all wrong.
Cite
@article{arxiv.2402.07447,
title = {Spectral asymptotics for linear elasticity with mixed boundary conditions},
author = {Genqian Liu},
journal= {arXiv preprint arXiv:2402.07447},
year = {2024}
}
Comments
12 pages