| Document Type
|
:
|
BL
|
| Record Number
|
:
|
954841
|
| Doc. No
|
:
|
b709211
|
| Main Entry
|
:
|
Ambrosio, Luigi.
|
| Title & Author
|
:
|
Gradient flows : : in metric spaces and in the space of probability measures /\ Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré.
|
| Publication Statement
|
:
|
Boston :: Birkhäuser,, 2005.
|
| Series Statement
|
:
|
Lectures in mathematics ETH Zürich
|
| Page. NO
|
:
|
1 online resource (vii, 333 pages) :: illustrations
|
| ISBN
|
:
|
3764324287
|
|
|
:
|
: 3764373091
|
|
|
:
|
: 9783764324285
|
|
|
:
|
: 9783764373092
|
|
|
:
|
9783764324284
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references (pages 321-329) and index.
|
| Contents
|
:
|
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.
|
| Abstract
|
:
|
"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.
|
| Subject
|
:
|
Differential equations, Parabolic.
|
| Subject
|
:
|
Evolution equations, Nonlinear.
|
| Subject
|
:
|
Measure theory.
|
| Subject
|
:
|
Metric spaces.
|
| Subject
|
:
|
Monotone operators.
|
| Subject
|
:
|
Équations d'évolution non linéaires.
|
| Subject
|
:
|
Équations différentielles paraboliques.
|
| Subject
|
:
|
Espaces métriques.
|
| Subject
|
:
|
Mesure, Théorie de la.
|
| Subject
|
:
|
Opérateurs monotones.
|
| Subject
|
:
|
Differential equations, Parabolic.
|
| Subject
|
:
|
Evolution equations, Nonlinear.
|
| Subject
|
:
|
MATHEMATICS-- Calculus.
|
| Subject
|
:
|
MATHEMATICS-- Mathematical Analysis.
|
| Subject
|
:
|
Measure theory.
|
| Subject
|
:
|
Metric spaces.
|
| Subject
|
:
|
Monotone operators.
|
| Subject
|
:
|
Differential equations, Parabolic.
|
| Subject
|
:
|
Evolution equations, Nonlinear.
|
| Subject
|
:
|
Measure theory.
|
| Subject
|
:
|
Metric spaces.
|
| Subject
|
:
|
Monotone operators.
|
| Dewey Classification
|
:
|
515/.42
|
| LC Classification
|
:
|
QA312.A58 2005
|
| NLM classification
|
:
|
31.40bcl
|
|
|
:
|
O174. 12clc
|
| Added Entry
|
:
|
Gigli, Nicola.
|
|
|
:
|
Savaré, Giuseppe.
|