Jerome Le Rousseau,Gilles Lebeau,Luc Robbiano
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II: General Boundary Conditions on Riemannian Manifolds
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II: General Boundary Conditions on Riemannian Manifolds
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- More about Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II: General Boundary Conditions on Riemannian Manifolds
This monograph explores the applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations,extending them to Riemannian manifolds and more general boundary conditions. It covers topics such as Lopatinskii-Sapiro boundary conditions,quantified unique continuation,logarithmic stabilization,and null-controllability of the heat equation.
Format: Hardback
Length: 547 pages
Publication date: 23 April 2022
Publisher: Springer Nature Switzerland AG
This monograph delves into the realm of Carleman estimates, exploring their applications in the study of stabilization and controllability properties of partial differential equations. In the first volume, these estimates were derived in regular open sets in Euclidean space and Dirichlet boundary conditions. However, in this second volume, they are extended to Riemannian manifolds and more general boundary conditions.
The book begins by examining Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, laying the foundation for deriving Carleman estimates for this operator on Riemannian manifolds. The subsequent chapters delve into various applications of Carleman estimates, including quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation.
Two additional chapters explore some advanced results on Carleman estimates.
The final part of the book is dedicated to exposition of necessary background material, encompassing elements of differential and Riemannian geometry, Sobolev spaces, and Laplace problems on Riemannian manifolds.
This comprehensive monograph provides a valuable resource for researchers and practitioners in the field of partial differential equations, offering insights into the applications of Carleman estimates and their significance in understanding the behavior of complex systems.
Weight: 1237g
Dimension: 254 x 178 (mm)
ISBN-13: 9783030886691
Edition number: 1st ed. 2022
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