The discrete spectrum of the Neumann-Poincaré operator in 3D elasticity
Artikel i vetenskaplig tidskrift, 2023

For the Neumann-Poincaré (double layer potential) operator in the three-dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the points of the essential spectrum and discuss geometric and mechanical meaning of coefficients in these formulas. In particular, we establish that for any body, there are infinitely many eigenvalues converging from above to each point of the essential spectrum. On the other hand, if there is a point where the boundary is concave (in particular, if the body contains cavities) then for each point of the essential spectrum there exists a sequence of eigenvalues converging to this point from below. The reasoning is based upon the representation of the Neumann-Poincaré operator as a zero order pseudodifferential operator on the boundary and the earlier results by the author on the eigenvalue asymptotics for polynomially compact pseudodifferential operators.

3D elasticity

Eigenvalue asymptotics

Neumann-Poincaré operator

Pseudodifferential operators

Författare

Grigori Rozenblioum

Chalmers, Matematiska vetenskaper

Saint Petersburg State University - Spsu

Journal of Pseudo-Differential Operators and Applications

1662-9981 (ISSN) 1662999x (eISSN)

Vol. 14 2 26

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s11868-023-00520-y

Mer information

Senast uppdaterat

2023-04-14