Two-term spectral asymptotics in linear elasticity

TL;DR

This paper derives the two-term spectral asymptotics for linear elasticity boundary value problems on smooth manifolds, correcting previous errors and providing illustrative examples and historical context.

Contribution

It establishes the two-term spectral asymptotics for linear elasticity problems on manifolds, correcting prior inaccuracies and including examples and a historical overview.

Findings

Derived two-term spectral asymptotics for linear elasticity

Corrected previous erroneous results in the literature

Provided illustrative examples and historical context

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].