arXiv:2112.07710 Abstract | arXiv Analytics

arXiv:2112.07710 [math.AP]Abstract References Reviews Resources

Aymptotics of eigenvalues of the Neumann-Poincar'e operator in 3D elasticity

Published 2021-12-14, updated 2022-12-05Version 2

We consider the Neumann-Poincar'e (double layer potential) operator in 3D elasicity on a smooth closed surface. Its essential spectrum consists of 3 points. We find the asymptotics of sequences of eigenvalues converging to these three pounts. They are expressed via the eigenvalue distribution for a matrix eigenvalue problem depending on the points of the cotangent bundle of the surface. For the two-sided asymptotics for the distribution of the the union of sequences of eigenvalues converging to the point of the essential spectrum from both sides, an expression is found via the Euler characteristics and the Willmore energy of the surface.

Comments: arXiv admin note: text overlap with arXiv:2006.10568 Ver.2, 2022.12.05 is an essentially extended version of Ver.1

Categories: math.AP, math.SP

Subjects: 35P20, 58J40, 58J50

Keywords: 3d elasticity, neumann-poincare operator, aymptotics, essential spectrum consists, matrix eigenvalue problem

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