Two-Term Spectral Asymptotics in Linear Elasticity

Matteo Capoferri; Leonid Friedlander; Michael Levitin; Dmitri Vassiliev

doi:10.1007/s12220-023-01269-y

Two-Term Spectral Asymptotics in Linear Elasticity

Matteo Capoferri
, Leonid Friedlander
, Michael Levitin
, Dmitri Vassiliev

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

41 Downloads (Pure)

Abstract

We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the subject. In particular, we correct erroneous results published by Liu (J Geom Anal 31:10164–10193, 2021).

Original language	English
Article number	242
Journal	Journal of Geometric Analysis
Volume	33
Issue number	8
Early online date	13 May 2023
DOIs	https://doi.org/10.1007/s12220-023-01269-y
Publication status	Published - Aug 2023

Keywords

74J05
Rayleigh waves
Dirichlet conditions
Eigenvalue counting function
Elasticity
Free boundary conditions
Primary 35P20
Secondary 35Q74

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title = "Two-Term Spectral Asymptotics in Linear Elasticity",

abstract = "We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the subject. In particular, we correct erroneous results published by Liu (J Geom Anal 31:10164{\textendash}10193, 2021).",

keywords = "74J05, Rayleigh waves, Dirichlet conditions, Eigenvalue counting function, Elasticity, Free boundary conditions, Primary 35P20, Secondary 35Q74",

author = "Matteo Capoferri and Leonid Friedlander and Michael Levitin and Dmitri Vassiliev",

note = "Funding Information: MC was partially supported by a Leverhulme Trust Research Project Grant RPG-2019-240, by a Research Grant (Scheme 4) of the London Mathematical Society, and by a grant of the Heilbronn Institute for Mathematical Research (HIMR) via the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences. ML was partially supported by the EPSRC grants EP/W006898/1 and EP/V051881/1 and by the University of Reading RETF Open Fund. All the support is gratefully acknowledged. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

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doi = "10.1007/s12220-023-01269-y",

language = "English",

volume = "33",

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AU - Capoferri, Matteo

AU - Friedlander, Leonid

AU - Levitin, Michael

AU - Vassiliev, Dmitri

N1 - Funding Information: MC was partially supported by a Leverhulme Trust Research Project Grant RPG-2019-240, by a Research Grant (Scheme 4) of the London Mathematical Society, and by a grant of the Heilbronn Institute for Mathematical Research (HIMR) via the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences. ML was partially supported by the EPSRC grants EP/W006898/1 and EP/V051881/1 and by the University of Reading RETF Open Fund. All the support is gratefully acknowledged. Publisher Copyright: © 2023, The Author(s).

PY - 2023/8

Y1 - 2023/8

N2 - We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the subject. In particular, we correct erroneous results published by Liu (J Geom Anal 31:10164–10193, 2021).

AB - We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the subject. In particular, we correct erroneous results published by Liu (J Geom Anal 31:10164–10193, 2021).

KW - 74J05

KW - Rayleigh waves

KW - Dirichlet conditions

KW - Eigenvalue counting function

KW - Elasticity

KW - Free boundary conditions

KW - Primary 35P20

KW - Secondary 35Q74

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DO - 10.1007/s12220-023-01269-y

M3 - Article

SN - 1050-6926

VL - 33

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 8

M1 - 242

ER -

Two-Term Spectral Asymptotics in Linear Elasticity

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