Elliptic Carleman Estimates and Applications to Stabilization and Controllability. General Boundary Conditions on Riemannian Manifolds

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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Gardado en:
Detalles Bibliográficos
Auteurs principaux: Le Rousseau, Jérôme, 19..-, Lebeau, Gilles, 1954- (Auteur), Robbiano, Luc, 1958- (Auteur)
Formato: Livre papier
Idioma:Anglais
Publicado: Cham : Birkhaüser C 2022.
Series:Progress in nonlinear differential equations and their applications. PNLDE subseries in control volume 98
Sujets:
Équations aux dérivées partielles
Analyse globale (mathématiques)
Riemann, Variétés de
Commande, Théorie de la
Autres localisations: Voir dans le Sudoc
Edition sous un autre format:• Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II, General Boundary Conditions on Riemannian Manifolds, by Jérôme Le Rousseau, 1st ed. 2022., 2022, Cham, Springer International Publishing, PNLDE Subseries in Control, 978-3-030-88670-7
Table des matières:
  • 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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