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arXiv · 1702.03415

Elastic Neumann-Poincar\'e operators on three dimensional smooth domains: Polynomial compactness and spectral structure

Kazunori Ando·Hyeonbae Kang·Yoshihisa Miyanishi
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Abstract

We prove that the elastic Neumann--Poincar\'e operator defined on the smooth boundary of a bounded domain in three dimensions, which is known to be non-compact, is in fact polynomially compact. As a consequence, we prove that the spectrum of the elastic Neumann-Poincar\'e operator consists of three non-empty sequences of eigenvalues accumulating to certain numbers determined by Lam\'e parameters. These results are proved using the surface Riesz transform, calculus of pseudo-differential operators and the spectral mapping theorem.

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Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi. 2017-02-11. Elastic Neumann-Poincar\'e operators on three dimensional smooth domains: Polynomial compactness and spectral structure. https://arxiv.org/abs/1702.03415

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