國立虎尾科技大學 |

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II = General Boundary Conditions on Riemannian Manifolds /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II/ by Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano.
Reminder of title:	General Boundary Conditions on Riemannian Manifolds /
Author:	Le Rousseau, Jérôme.
other author:	Lebeau, Gilles.
Description:	IX, 547 p. 17 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Differential equations. -
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, Jérôme.

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume IIGeneral Boundary Conditions on Riemannian Manifolds /[electronic resource] :by Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano. - 1st ed. 2022. - IX, 547 p. 17 illus., 9 illus. in color.online resource. - PNLDE Subseries in Control,982731-7374 ;. - PNLDE Subseries in Control,97.

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:

527664
Differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.35

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II = General Boundary Conditions on Riemannian Manifolds /
LDR:03947nam a22004095i 4500 001 1093070
003 DE-He213
005 20220422053403.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783030886707 $9 978-3-030-88670-7
024 7 $a 10.1007/978-3-030-88670-7 $2 doi
035 $a 978-3-030-88670-7
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
100 1 $a Le Rousseau, Jérôme. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1398962
245 1 0 $a Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II $h [electronic resource] : $b General Boundary Conditions on Riemannian Manifolds / $c by Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2022.
300 $a IX, 547 p. 17 illus., 9 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a PNLDE Subseries in Control, $x 2731-7374 ; $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 Differential equations. $3 527664
650 0 $a Global analysis (Mathematics). $3 1255807
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a System theory. $3 566168
650 0 $a Control theory. $3 527674
650 0 $a Operator theory. $3 527910
650 1 4 $a Differential Equations. $3 681826
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Systems Theory, Control . $3 1366058
650 2 4 $a Operator Theory. $3 672127
700 1 $a Lebeau, Gilles. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1398963
700 1 $a Robbiano, Luc. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1390726
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030886691
776 0 8 $i Printed edition: $z 9783030886714
776 0 8 $i Printed edition: $z 9783030886721
830 0 $a PNLDE Subseries in Control, $x 2731-7374 ; $v 97 $3 1398964
856 4 0 $u https://doi.org/10.1007/978-3-030-88670-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)