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Analysis and PDE Seminar

Date:
-
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Professor Plamen Stefanov, Purdue University
TITLE: Traveltime Tomography with local data
 
ABSTRACT: We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a xed point on the boundary. We show that one can recover a conformal factor near a strictly convex point where we have the information, uniquely and in a stable way. In
particular, this implies that we can determine locally the isotropic sound speed of a medium by measuring the travel times of waves joining points close to a convex point on the boundary.  The local results lead to a global lens rigidity uniqueness and stability result assuming that the manifold is foliated by strictly convex hypersurfaces.
 
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