Overview
- Explores applications of Carleman estimates to study stabilization and controllability properties of PDEs
- Covers all necessary background material in detail
- Complemented by a second volume that extends treatment to Riemannian manifolds
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 98)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (18 chapters)
-
Front Matter
-
General Boundary Conditions
-
Front Matter
-
-
Carleman Estimates on Riemannian Manifolds
-
Front Matter
-
-
Further Aspects of Carleman Estimates
-
Front Matter
-
-
Background Material: Geometry
-
Front Matter
-
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
Book Subtitle: General Boundary Conditions on Riemannian Manifolds
Authors: Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-030-88670-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-88669-1Published: 23 April 2022
Softcover ISBN: 978-3-030-88672-1Published: 23 April 2023
eBook ISBN: 978-3-030-88670-7Published: 22 April 2022
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: IX, 547
Number of Illustrations: 8 b/w illustrations, 9 illustrations in colour
Topics: Analysis, Global Analysis and Analysis on Manifolds, Systems Theory, Control, Operator Theory