Eigenvalue asymptotics for polynomially compact pseudodifferenial operators and applications

TL;DR

This paper derives the asymptotic behavior of eigenvalues for polynomially compact zero order pseudodifferential operators, with applications to the Neumann-Poincaré operator in linear elasticity.

Contribution

It provides new eigenvalue asymptotics for a class of polynomially compact pseudodifferential operators, including the Neumann-Poincaré operator.

Findings

Eigenvalue asymptotics for polynomially compact operators derived

Applications to linear elasticity problems demonstrated

Neumann-Poincaré operator eigenvalues characterized asymptotically

Abstract

We fnd the asymptotics of eigenvalues of polynomially compact zero order pseudodiferential operators, the motivating example being the Neumann- Poincare operator in linear elasticity.