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001446150 001__ 1446150
001446150 003__ OCoLC
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001446150 020__ $$a9783030886707$$q(electronic bk.)
001446150 020__ $$a3030886700$$q(electronic bk.)
001446150 020__ $$z9783030886691$$q(print)
001446150 0247_ $$a10.1007/978-3-030-88670-7$$2doi
001446150 035__ $$aSP(OCoLC)1312638005
001446150 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dOCLCO$$dOCLCF$$dOCLCQ
001446150 049__ $$aISEA
001446150 050_4 $$aQA331
001446150 08204 $$a512.7/3$$223/eng/20220426
001446150 1001_ $$aLe Rousseau, Jérôme,$$eauthor.
001446150 24510 $$aElliptic Carleman estimates and applications to stabilization and controllability.$$n, Volume II,$$pGeneral boundary conditions on Riemannian manifolds /$$cJérôme Le Rousseau, Gilles Lebeau, Luc Robbiano.
001446150 24630 $$aGeneral boundary conditions on Riemannian manifolds
001446150 264_1 $$aCham, Switzerland :$$bBirkhäuser,$$c2022.
001446150 300__ $$a1 online resource (ix, 547 pages) :$$billustrations (some color).
001446150 336__ $$atext$$btxt$$2rdacontent
001446150 337__ $$acomputer$$bc$$2rdamedia
001446150 338__ $$aonline resource$$bcr$$2rdacarrier
001446150 4901_ $$aProgress in nonlinear differential equations and their applications, PNLDE subseries in control,$$x2731-7374 ;$$vvolume 98
001446150 504__ $$aIncludes bibliographical references and indexes.
001446150 5050_ $$aIntroduction -- Part 1: General Boundary Conditions -- Lopatinskii-Sapiro Boundary Conditions -- Fredholm Properties of Second-Order Elliptic Operators -- Selfadjoint Operators under General Boundary Conditions -- Part 2: Carleman Estimates on Riemannian Manifolds -- Estimates on Riemannian Manifolds for Dirichlet Boundary Conditions -- Pseudo-Differential Operators on a Half-Space -- Sobolev Norms with a Large Parameter on a Manifold -- Estimates for General Boundary Conditions -- Part 3: Applications -- Quantified Unique Continuation on a Riemannian Manifold -- Stabilization of Waves under Neumann Boundary Damping -- Spectral Inequality for General Boundary Conditions and Applications -- Part 4: Further Aspects of Carleman Estimates -- Carleman Estimates with Source Terms of Weaker Regularity -- Optimal Estimates at the Boundary -- Background Material: Geometry -- Elements of Differential Geometry -- Integration and Differential Operators on Manifolds -- Elements of Riemannian Geometry -- Sobolev Spaces and Laplace Problems on a Riemannian Manifold -- Bibliography -- Index -- Index of Notation.
001446150 506__ $$aAccess limited to authorized users.
001446150 520__ $$aThis monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
001446150 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 26, 2022).
001446150 650_0 $$aCarleman theorem.
001446150 650_0 $$aRiemannian manifolds.
001446150 650_0 $$aBoundary value problems.
001446150 650_6 $$aMéthode de Carleman.
001446150 650_6 $$aVariétés de Riemann.
001446150 650_6 $$aProblèmes aux limites.
001446150 655_0 $$aElectronic books.
001446150 7001_ $$aLebeau, Gilles,$$eauthor.
001446150 7001_ $$aRobbiano, Luc,$$eauthor.
001446150 830_0 $$aProgress in nonlinear differential equations and their applications.$$pPNLDE subseries in control ;$$vv. 98.
001446150 852__ $$bebk
001446150 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88670-7$$zOnline Access$$91397441.1
001446150 909CO $$ooai:library.usi.edu:1446150$$pGLOBAL_SET
001446150 980__ $$aBIB
001446150 980__ $$aEBOOK
001446150 982__ $$aEbook
001446150 983__ $$aOnline
001446150 994__ $$a92$$bISE