東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Elliptic carleman estimates and appl...

Le Rousseau, Jerome.

Linked to FindBook

Google Book

Amazon

博客來

Elliptic carleman estimates and applications to stabilization and controllability.. Volume II,. General boundary conditions on Riemannian manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic carleman estimates and applications to stabilization and controllability./ by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
remainder title:	General boundary conditions on Riemannian manifolds
Author:	Le Rousseau, Jerome.
other author:	Lebeau, Gilles.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	ix, 547 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Carleman theorem. -
Online resource:	https://doi.org/10.1007/978-3-030-88670-7
ISBN:	9783030886707

Elliptic carleman estimates and applications to stabilization and controllability.. Volume II,. General boundary conditions on Riemannian manifolds
Le Rousseau, Jerome.

Elliptic carleman estimates and applications to stabilization and controllability.Volume II,General boundary conditions on Riemannian manifolds[electronic resource] /General boundary conditions on Riemannian manifoldsby Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano. - Cham :Springer International Publishing :2022. - ix, 547 p. :ill. (some col.), digital ;24 cm. - PNLDE subseries in control,v. 982731-7374 ;. - PNLDE subseries in control ;v. 98..

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.

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 the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: 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 consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.

ISBN: 9783030886707

Standard No.: 10.1007/978-3-030-88670-7doiSubjects--Topical Terms:

3270405
Carleman theorem.

LC Class. No.: QA331 / .L4 2022

Dewey Class. No.: 512.73

Elliptic carleman estimates and applications to stabilization and controllability.. Volume II,. General boundary conditions on Riemannian manifolds
LDR:03641nmm a2200349 a 4500 001 2300682
003 DE-He213
005 20220422053403.0
006 m d
007 cr nn 008maaau
008 230324s2022 sz s 0 eng d
020 $a 9783030886707 $q (electronic bk.)
020 $a 9783030886691 $q (paper)
024 7 $a 10.1007/978-3-030-88670-7 $2 doi
035 $a 978-3-030-88670-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331 $b .L4 2022
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 512.73 $2 23
090 $a QA331 $b .L617 2022
100 1 $a Le Rousseau, Jerome. $3 3596422
245 1 0 $a Elliptic carleman estimates and applications to stabilization and controllability. $n Volume II, $p General boundary conditions on Riemannian manifolds $h [electronic resource] / $c by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
246 3 0 $a General boundary conditions on Riemannian manifolds
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2022.
300 $a ix, 547 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a PNLDE subseries in control, $x 2731-7374 ; $v v. 98
505 0 $a 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.
520 $a 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 the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: 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 consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
650 0 $a Carleman theorem. $3 3270405
650 0 $a Riemannian manifolds. $3 540526
650 0 $a Boundary value problems. $3 527599
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Operator Theory. $3 897311
700 1 $a Lebeau, Gilles. $3 716632
700 1 $a Robbiano, Luc. $3 3596423
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a PNLDE subseries in control ; $v v. 98. $3 3599426
856 4 0 $u https://doi.org/10.1007/978-3-030-88670-7
950 $a Mathematics and Statistics (SpringerNature-11649)