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Spectral asymptotics for linear elasticity with mixed boundary conditions

Genqian Liu

Abstract

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.

Spectral asymptotics for linear elasticity with mixed boundary conditions

Abstract

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.
Paper Structure (3 sections, 66 equations)

This paper contains 3 sections, 66 equations.

Table of Contents

  1. Introduction
  2. Asymptotic formulae for the mixed boundary conditions
  3. Numerical verifications

Theorems & Definitions (1)

  • proof