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Séminaire Math-Phys : L^p resolvent estimates for elliptic operators on compact manifolds and applications

Mercredi 21 juin 11:00-12:00 - Katya Krupchyk - University of California, Irvine

Séminaire Math-Phys : L^p resolvent estimates for elliptic operators on compact manifolds and applications

Résumé : We shall discuss uniform L^p resolvent estimates for elliptic operators. Originally obtained by Kenig, Ruiz, and Sogge in the case of the Euclidean space, they have been established by Shen for the flat torus and by Dos Santos Ferreira, Kenig, and Salo for general compact manifolds, in the case of the Laplacian. We shall discuss an extension to the case of higher order self-adjoint operators, as well as to some weakly non-self-adjoint operators, such as the stationary damped wave operator. Our approach is based on the techniques of semiclassical Strichartz estimates. Applications to spectral theory for periodic Schrodinger operators as well as to inverse boundary problems for elliptic operators with coefficients of low regularity will be presented. This talk is based on joint works with Gunther Uhlmann and with Nicolas Burq and David Dos Santos Ferreira.

Lieu : Salle A318

Pour en savoir plus sur cet événement, consultez l'article Séminaires Math-Physique