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- W4328052209 abstract "Abstract For the Neumann-Poincaré (double layer potential) operator in the three-dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the points of the essential spectrum and discuss geometric and mechanical meaning of coefficients in these formulas. In particular, we establish that for any body, there are infinitely many eigenvalues converging from above to each point of the essential spectrum. On the other hand, if there is a point where the boundary is concave (in particular, if the body contains cavities) then for each point of the essential spectrum there exists a sequence of eigenvalues converging to this point from below. The reasoning is based upon the representation of the Neumann-Poincaré operator as a zero order pseudodifferential operator on the boundary and the earlier results by the author on the eigenvalue asymptotics for polynomially compact pseudodifferential operators." @default.
- W4328052209 created "2023-03-22" @default.
- W4328052209 creator A5043371527 @default.
- W4328052209 date "2023-03-21" @default.
- W4328052209 modified "2023-10-14" @default.
- W4328052209 title "The discrete spectrum of the Neumann-Poincaré operator in 3D elasticity" @default.
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- W4328052209 doi "https://doi.org/10.1007/s11868-023-00520-y" @default.
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