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Session S33 - Spectral Geometry

Monday, July 12, 12:30 ~ 12:50 UTC-3

Anisotropic inverse problems for elliptic PDE

Katya Krupchyk

University of California, Irvine , USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we shall discuss some recent progress on inverse boundary problems for linear and nonlinear elliptic PDE on Riemannian manifolds. In particular, we shall show that the presence of a nonlinearity may help, allowing one to solve inverse problems for nonlinear equations in situations where the linear counterpart is open. We shall also present a solution of the linearized anisotropic Calderon problem on transversally anisotropic manifolds, under the assumption that the transversal manifold is real analytic and satisfies a certain condition related to the geometry of pairs of intersecting geodesics. The argument depends on a construction of Gaussian beam quasimodes on the transversal manifold, with exponentially small errors. This talk is based on joint works with Tony Liimatainen, Mikko Salo, and Gunther Uhlmann.

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