TY  - GEN
N2  - This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
DO  - 10.1007/978-3-030-88670-7
DO  - doi
AB  - This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
T1  - Elliptic Carleman estimates and applications to stabilization and controllability.
AU  - Le Rousseau, Jérôme,
AU  - Lebeau, Gilles,
AU  - Robbiano, Luc,
VL  - volume 98
CN  - QA331
ID  - 1446150
KW  - Carleman theorem.
KW  - Riemannian manifolds.
KW  - Boundary value problems.
KW  - Méthode de Carleman.
KW  - Variétés de Riemann.
KW  - Problèmes aux limites.
SN  - 9783030886707
SN  - 3030886700
TI  - Elliptic Carleman estimates and applications to stabilization and controllability.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88670-7
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88670-7
ER  -