Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
portes grátis
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
General Boundary Conditions on Riemannian Manifolds
Le Rousseau, Jerome; Robbiano, Luc; Lebeau, Gilles
Springer Nature Switzerland AG
04/2022
547
Dura
Inglês
9783030886691
15 a 20 dias
1237
Descrição não disponível.
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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Elliptic Carleman estimates;Lopatinskii-Sapiro boundary conditions;Stabilization and Controllability Properties of PDEs;Logarithmic stabilization of the wave equation;Null-controllability of the heat equation
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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