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Lundi 12 juin 2017
Hoai-Minh Nguyen (EPFL, Lausanne)
On the discreteness of the interior transmission eigenvalues for acoustic waves
Abstract : Interior transmission eigenvalues for acoustic waves is an eigenvalue problem involving two scalar elliptic equations of two unknowns which have the same Neumann and Dirichlet boundary conditions. One of its interests comes from the connection with the density of the range of the far field operator in the scattering problem. The interior transmission eigenvalue problem is known to be not self-adjoint. More severely, a priori estimates are non-standard and do not hold in general in this context. In this talk, I will review know results on the discreteness of transmissions eigenvalues and discuss new ones (joint work with Q. H Nguyen).