Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II General Boundary Conditions on Riemannian Manifolds / by Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano.

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II General Boundary Conditions on Riemannian Manifolds /

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 th...

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Bibliographic Details
Main Authors: Le Rousseau, Jérôme (Author), Lebeau, Gilles (Author), Robbiano, Luc (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2022.
Edition:1st ed. 2022.
Series:Progress in nonlinear differential equations and their applications. PNLDE subseries in control ; 98.
Subjects:
Differential equations.
Global analysis (Mathematics)
Manifolds (Mathematics)
System theory.
Control theory.
Operator theory.
Online Access: Full text (Wentworth users only)
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 Spaces and Laplace Problems on a Riemannian Manifold
  • Bibliography
  • Index
  • Index of Notation.

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