Surface Riesz transforms and spectral property of elastic Neumann--Poincaé operators on less smooth domains in three dimensions

Abstract

It is known that the Neumann--Poincaré operator for the Lamé system of linear elasticity is polynomially compact and, as a consequence, that its spectrum consists of three non-empty sequences of eigenvalues accumulating to certain numbers determined by Lamé parameters, if the boundary of the domain where the operator is defined is $C^{\infty }$-smooth. We extend this result to less smooth boundaries, namely, $C^{1,\alpha }$-smooth boundaries for some $\alpha >0$. The results are obtained by proving certain identities for surface Riesz transforms, which are singular integral operators of nonconvolution type, defined by the matrix tensor on a given surface.

arXiv comment14 pages

References in corpus (1)

• Characterization of the essential spectrum of the Neumann-Poincaré operator in 2D domains with corner via Weyl sequences

Cited by in corpus (4)

• Spectral analysis of Neumann-Poincaré operator
• Spectral properties of the Neumann-Poincaré operator in 3D elasticity
• Convergence rate for eigenvalues of the elastic Neumann--Poincaré operator on smooth and real analytic boundaries in two dimensions
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