Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II

General Boundary Conditions on Riemannian Manifolds

AvJérôme Le Rousseau,Gilles Lebeau

Häftad, Engelska, 2023

Del 98 i serien Progress in Nonlinear Differential Equations and Their Applications

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-04-23
Mått:178 x 254 x 30 mm
Vikt:1 040 g
Format:Häftad
Språk:Engelska
Serie:Progress in Nonlinear Differential Equations and Their Applications
Antal sidor:547
Förlag:Springer Nature Switzerland AG
ISBN:9783030886721

Utforska kategorier

Innehållsförteckning

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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