in metric spaces and in the space of probability measures /
First Statement of Responsibility
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Boston :
Name of Publisher, Distributor, etc.
Birkhäuser,
Date of Publication, Distribution, etc.
2005.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (vii, 333 pages) :
Other Physical Details
illustrations
SERIES
Series Title
Lectures in mathematics ETH Zürich
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (pages 321-329) and index.
CONTENTS NOTE
Text of Note
1. Curves and gradients in metric spaces -- 2. Existence of curves of maximal slope and their variational approximation -- 3. Proofs of the convergence theorems -- 4. Uniqueness, generation of contraction semigroups, error estimates -- 5. Preliminary results on measure theory -- 6. The optimal transportation problem -- 7. The Wasserstein distance and its behaviour along geodesics -- 8. A.C. curves in P[subscript p](X) and the continuity equation -- 9. Convex functionals in P[subscript p](X) -- 10. Metric slope and subdifferential calculus in P[subscript p](X) -- 11. Gradient flows and curves of maximal slope in P[subscript p](X) -- 12. Appendix.
0
SUMMARY OR ABSTRACT
Text of Note
"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."--Jacket.