Elastic Neumann-Poincaré operators on three dimensional smooth domains: Polynomial compactness and spectral structure

2017/02/11 by Ando, Kazunori, Kang, Hyeonbae, Miyanishi, Yoshihisa · 1 citation
#35J47 (Primary) #35P05 (Secondary) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1702.03415

Abstract

We prove that the elastic Neumann--Poincaré 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-Poincaré operator consists of three non-empty sequences of eigenvalues accumulating to certain numbers determined by Lamé parameters. These results are proved using the surface Riesz transform, calculus of pseudo-differential operators and the spectral mapping theorem.

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