Carleman Estimates and Applications to Uniqueness and Control Theory

Consists of expository articles and research papers highlighting new results on Carleman estimates and their applications. Focus is on unique continuation, control theory, and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail. Also examined are applications of Carleman estimates to stabilization, observability, and exact control for the wave and the Schrodinger equations. Includes open problems on the controllability of linear and semilinear heat equations. Of interest to researchers and graduate students of pdes and their applications.

Klappentext

The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla­ bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con­ trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza­ tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control­ lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac­ cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.

Inhalt
Stabilization for the Wave Equation on Exterior Domains.- Carleman Estimate and Decay Rate of the Local Energy for the Neumann Problem of Elasticity.- Microlocal Defect Measures for Systems.- Strong Uniqueness for Laplace and Bi-Laplace Operators in the Limit Case.- Stabilization for the Semilinear Wave Equation in Bounded Domains.- Recent Results on Unique Continuation for Second Order Elliptic Equations.- Strong Uniqueness for Fourth Order Elliptic Differential Operators.- Second Microlocalization Methods for Degenerate CauchyRiemann Equations.- A Gärding Inequality on a Manifold with Boundary.- Some Necessary Conditions for Hyperbolic Systems.- Strong Unique Continuation Property for First Order Elliptic Systems.- Observability of the Schrödinger Equation.- Unique Continuation from Sets of Positive Measure.- Some Results and Open Problems on the Controllability of Linear and Semilinear Heat Equations.