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Carleman estimates and their applications to inverse problems and control theory.
by
Victor Isakov
Wichita State University, Wichita, U.S.A.
We give a review of weighted estimates in Sobolev spaces for scalar partial differential equations and systems. A special emphasis is on recent results on dynamical elasticity systems and use of spaces of negative order. We discuss applications to uniqueness and stability of the continuation, in particular, Holmgren-John-Tataru theorem on sharp uniqueness domains for time independent coefficients. We review applications to approximate and exact controllability for such equations and systems. Finally we focus on use of Carleman estimates to show uniqueness and stability in determining time independent coefficients of hyperbolic equations and systems from lateral boundary overdetermination. We report on the results of Bukhgeim, Imanuvilov, Klibanov, Lasiecka, Triggiani, Yamamoto, and of the speaker.
Date received: May 19, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqw-55.