Two-term spectral asymptotics in linear elasticity
Spectral Theory
2024-04-16 v3 Analysis of PDEs
Differential Geometry
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 in [J. Geom. Anal. 31 (2021), 10164--10193].
Cite
@article{arxiv.2207.13636,
title = {Two-term spectral asymptotics in linear elasticity},
author = {Matteo Capoferri and Leonid Friedlander and Michael Levitin and Dmitri Vassiliev},
journal= {arXiv preprint arXiv:2207.13636},
year = {2024}
}
Comments
37 pages, 10 figures. This version corrects typesetting misprints in formula (B.6) in the previous arXiv and published versions. These misprints do not affect the rest of the paper. Authors' computational scripts are available at https://michaellevitin.net/elasticity.html