Convergence rate for eigenvalues of the elastic Neumann--Poincar\'e operator on smooth and real analytic boundaries in two dimensions
Spectral Theory
2019-03-19 v1
Abstract
The elastic Neumann--Poincar\'e operator is a boundary integral operator associated with the Lam\'e system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two different points determined by Lam\'e parameters. We show that eigenvalues converge at a polynomial rate on smooth boundaries and the convergence rate is determined by smoothness of the boundary. We also show that they converge at an exponential rate if the boundary of the domain is real analytic.
Keywords
Cite
@article{arxiv.1903.07084,
title = {Convergence rate for eigenvalues of the elastic Neumann--Poincar\'e operator on smooth and real analytic boundaries in two dimensions},
author = {Kazunori Ando and Hyeonbae Kang and Yoshihisa Miyanishi},
journal= {arXiv preprint arXiv:1903.07084},
year = {2019}
}
Comments
19 pages