English

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

R2 v1 2026-06-28T14:45:41.619Z