Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
General Boundary Conditions on Riemannian Manifolds
Series: Progress in Nonlinear Differential Equations and Their Applications; 98;
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Product details:
- Edition number 1st ed. 2022
- Publisher Birkhäuser
- Date of Publication 23 April 2023
- Number of Volumes 1 pieces, Book
- ISBN 9783030886721
- Binding Paperback
- No. of pages547 pages
- Size 254x178 mm
- Weight 1053 g
- Language English
- Illustrations 8 Illustrations, black & white; 9 Illustrations, color 506
Categories
Short description:
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.
Long description:
Table of Contents:
Introduction.- Part 1: General Boundary Conditions.- Lopatinskii-Sapiro Boundary Conditions.- Fredholm Properties of Second-Order Elliptic Operators.- Selfadjoint Operators under General Boundary Conditions.- Part 2: Carleman Estimates on Riemannian Manifolds.- Estimates on Riemannian Manifolds for Dirichlet Boundary Conditions.- Pseudo-Differential Operators on a Half-Space.- Sobolev Norms with a Large Parameter on a Manifold.- Estimates for General Boundary Conditions.- Part 3: Applications.- Quantified Unique Continuation on a Riemannian Manifold.- Stabilization of Waves under Neumann Boundary Damping.- Spectral Inequality for General Boundary Conditions and Applications.- Part 4: Further Aspects of Carleman Estimates.- Carleman Estimates with Source Terms of Weaker Regularity.- Optimal Estimates at the Boundary.- Background Material: Geometry.- Elements of Differential Geometry.- Integration and Differential Operators on Manifolds.- Elements of Riemannian Geometry.- Sobolev Spacesand Laplace Problems on a Riemannian Manifold.- Bibliography.- Index.- Index of Notation.
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