Spectral asymptotics for linear elasticity: the case of mixed boundary conditions

Matteo Capoferri; Isabel Mann

doi:10.1017/prm.2024.65

Spectral asymptotics for linear elasticity: the case of mixed boundary conditions

Matteo Capoferri
, Isabel Mann

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Abstract

We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two and three, thus verifying our general formulae both analytically and numerically.

Original language	English
Pages (from-to)	486-515
Number of pages	30
Journal	Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume	156
Issue number	2
Early online date	24 May 2024
DOIs	https://doi.org/10.1017/prm.2024.65
Publication status	Published - Apr 2026

Keywords

elasticity
eigenvalue counting function
Dirichlet conditions
free boundary conditions
mixed boundary conditions

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abstract = "We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two and three, thus verifying our general formulae both analytically and numerically.",

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KW - elasticity

KW - eigenvalue counting function

KW - Dirichlet conditions

KW - free boundary conditions

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DO - 10.1017/prm.2024.65

M3 - Article

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Spectral asymptotics for linear elasticity: the case of mixed boundary conditions

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