The Resource Gradient flows : in metric spaces and in the space of probability measures, Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
Gradient flows : in metric spaces and in the space of probability measures, Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
 Summary
 This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the KantorovichRubinsteinWasserstein distance. The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in nonsmooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability
 Language
 eng
 Edition
 2nd ed
 Extent
 1 online resource (vii, 334 pages)
 Contents

 1. Introduction
 Part I. Gradient flow in metric spaces
 2. Curves and gradients in metric spaces
 3. Existence of curves of maximal slope
 4. Proofs of the convergence theorems
 5. Generation of contraction semigroups
 Part II. Gradient flow in the Wasserstein spaces of probability measures
 6. Preliminary results on measure theory
 7. The optimal transportation problem
 8. The Wasserstein distance and its behaviour along geodesics
 9. A.c. curves and the continuity equation
 10. Convex functionals
 11. Metric slope and subdifferential calculus
 12. Gradient flows and curves of maximal slope
 13. Appendix
 Bibliography
 Isbn
 9783764387228
 Label
 Gradient flows : in metric spaces and in the space of probability measures
 Title
 Gradient flows
 Title remainder
 in metric spaces and in the space of probability measures
 Statement of responsibility
 Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
 Language
 eng
 Summary
 This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the KantorovichRubinsteinWasserstein distance. The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in nonsmooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability
 Cataloging source
 GW5XE
 Dewey number
 515/.42
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA312
 LC item number
 .A58 2008eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Lectures in mathematics ETH Zürich
 Label
 Gradient flows : in metric spaces and in the space of probability measures, Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
 Bibliography note
 Includes bibliographical references (pages 321331) and index
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1. Introduction  Part I. Gradient flow in metric spaces  2. Curves and gradients in metric spaces  3. Existence of curves of maximal slope  4. Proofs of the convergence theorems  5. Generation of contraction semigroups  Part II. Gradient flow in the Wasserstein spaces of probability measures  6. Preliminary results on measure theory  7. The optimal transportation problem  8. The Wasserstein distance and its behaviour along geodesics  9. A.c. curves and the continuity equation  10. Convex functionals  11. Metric slope and subdifferential calculus  12. Gradient flows and curves of maximal slope  13. Appendix  Bibliography
 Control code
 ocn304564764
 Dimensions
 unknown
 Edition
 2nd ed
 Extent
 1 online resource (vii, 334 pages)
 Form of item
 online
 Isbn
 9783764387228
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783764387228
 Other physical details
 illustrations
 http://library.link/vocab/ext/overdrive/overdriveId
 9783764387211
 http://library.link/vocab/recordID
 .b23820196
 Specific material designation
 remote
 System control number

 (OCoLC)304564764
 pebcs3764387211
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