Rayleigh-type Surface Quasimodes in General Linear Elasticity

Details Rayleigh-type Surface Quasimodes in General Linear Elasticity Rayleigh-type Surface Quasimodes in General Linear Elasticity

2010-08-17

arxiv.org/abs/1008.2930v2

Analysis & PDE 4-3 (2011) 461-497

Mathematics

Analysis of PDEs

46 pages. Corrected a Lipschitz estimate and the proof of Proposition 21

Scientific paper

10.2140/apde.2011.4.461

Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudo-differential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

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