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Katya Krupchyk

Lp resolvent estimates for elliptic operators on compact manifolds and applications

Abstract: We shall discuss uniform Lp resolvent estimates for elliptic operators. Originally obtained by Kenig, Ruiz, and Sogge in the case of the Euclidean space, they have been established by Dos Santos Ferreira, Kenig, and Salo for the Laplacian on a compact manifold. 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 low regularity coefficients will also be discussed. This talk is based on joint works with Gunther Uhlmann and with Nicolas Burq and David Dos Santos Ferreira.