Periodic elastic layer: spectral gaps and discrete spectrum

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Date(s) - 08/07/2015
14 h 00 min - 15 h 00 min


The spectrum of the Dirichlet of the isotropic elasticity system in a periodic layer will be asymptotically described. Such problem appears as a model problem for a thin periodic elastic gasket between two hard  clamped bodies with rough surfaces. Under certain geometric assumptions on the profile of the layer it is shown that any given number of spectral gaps can be opened as well as, by a local shape perturbations, any presctribed number of isolated eigenvalues in any fixed non-empty gap can be constructed. Several open questions on the spectrum of similar problems are formulated.


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