Elastic Neumann-Poincare Operators on Three Dimensional Smooth Domains: Polynomial Compactness and Spectral Structure

초록

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

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