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

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
Creator
Contributor
Subject
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 Kantorovich-Rubinstein-Wasserstein 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 non-smooth 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
Member of
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
Publication
Bibliography note
Includes bibliographical references (pages 321-331) 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
10.1007/978-3-7643-8722-8
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-3-7643-8721-1
http://library.link/vocab/recordID
.b23820196
Specific material designation
remote
System control number
  • (OCoLC)304564764
  • pebcs3764387211

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
Processing Feedback ...