Spectral asymptotics for linear elasticity with mixed boundary conditions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914674774114304 |
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| author | Liu, Genqian |
| author_facet | Liu, Genqian |
| contents | 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. Ørsted 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral asymptotics for linear elasticity with mixed boundary conditions Liu, Genqian Analysis of PDEs Differential Geometry Spectral Theory 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. Ørsted 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. |
| title | Spectral asymptotics for linear elasticity with mixed boundary conditions |
| topic | Analysis of PDEs Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2402.07447 |