PDE Seminar Abstracts

Applications of semiclassical resolvents to tomography problems

Leo Tzou
University of Sydney
Mon 24th Feb 2020, 2-3pm, Carslaw Room 829 (AGR)


A classical result of Jerison-Kenig showed that the optimal assumption for unique continuation properties for elliptic PDE. In this talk we will explore its connection to image reconstruction with impedance tomography. We will develop an analogous theory in the context of partial data inverse problems to obtain the same sharp regularity assumption as Jerison-Kenig. The method we use involves explicit microlocal construction of the Dirichlet Green’s function which on its own may be of interest for partial data image reconstruction.