Gradient Flows : in Metric Spaces and in the Space of Probability Measures
In this edition we made minor corrections kindly pointed out to us by some c- leagues, and we updated and expanded the bibliography. We have not included the developments of the theory of gradient ?ows occurred in the last three years, asgradient?ows inspaceswith Alexandrovcurvaturebounds [135] (see...
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| Format: | Livre numérique |
| Sprog: | Anglais |
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Basel :
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Cham : Springer Nature |
| Udgivelse: | Version électronique de la seconde édition. |
| Serier: | Lectures in Mathematics ETH Zürich
Lectures in Mathematics. ETH Zürich |
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l'impression du document génère 322 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
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| Edition sous un autre format: | • Gradient flows, in metric spaces and in the space of probability measures, Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré, 2nd edition, 2008, Basel, Birkhäuser, 1 vol. (VII-334 p.), Lectures in mathematics ETH Zürich, 978-3-7643-8721-1 |
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| 084 | |a 28A33. 2010 | ||
| 084 | |a 28A50. 2010 | ||
| 084 | |a 35K55. 2010 | ||
| 084 | |a 35K90. 2010 | ||
| 084 | |a 47H05. 2010 | ||
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| 100 | 1 | |a Ambrosio, Luigi, |d 1963-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Gradient Flows : |b in Metric Spaces and in the Space of Probability Measures |c Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré. |
| 250 | |a Version électronique de la seconde édition. | ||
| 260 | |a Basel : |b Birkhäuser Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lectures in Mathematics ETH Zürich | |
| 490 | 0 | |a Lectures in Mathematics. ETH Zürich | |
| 500 | |a l'impression du document génère 322 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Notation Notation Gradient Flow in Metric Spaces Curves and Gradients in Metric Spaces Existence of Curves of Maximal Slope and their Variational Approximation Proofs of the Convergence Theorems Uniqueness, Generation of Contraction Semigroups, Error Estimates Gradient Flow in the Space of Probability Measures Preliminary Results on Measure Theory The Optimal Transportation Problem The Wasserstein Distance and its Behaviour along Geodesics Absolutely Continuous Curves in p(X) and the Continuity Equation Convex Functionals in p(X) Metric Slope and Subdifferential Calculus in (X) Gradient Flows and Curves of Maximal Slope in p(X) | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a In this edition we made minor corrections kindly pointed out to us by some c- leagues, and we updated and expanded the bibliography. We have not included the developments of the theory of gradient ?ows occurred in the last three years, asgradient?ows inspaceswith Alexandrovcurvaturebounds [135] (see also[119]) and Fokker-Planck equations in in?nite-dimensional spaces [18], largely based on the ideas developed in the book. We also mention the long survey paper [17], more focussed on gradient ?ows in Euclidean spaces with respect to the quadratic Wasserstein distance, where the notion of Evolution Variational Inequality is d- cussed more in detail, and the monumental book of C. Villani [147], which will surely become the standard reference for the theory of Optimal Transport and its applications to geometry and PDE s. Pisa and Pavia, January 2008 Introduction This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 devoted to gradient ?ows in the L -Wasserstein space of probability measures on 2 a separableHilbert space X endowedwith the WassersteinL metric (we consider p the L -Wasserstein distance, p? (1,?), as well) | ||
| 650 | |a Espaces métriques | ||
| 650 | |a Théorie de la mesure | ||
| 650 | |a Opérateurs monotones | ||
| 650 | |a Équations d'évolution non linéaires | ||
| 650 | |a Équations différentielles paraboliques | ||
| 700 | 1 | |a Gigli, Nicola, |d 1974-...., |c mathématicien. |4 aut | |
| 700 | 1 | |a Savaré, Giuseppe, |d 1966- |4 aut | |
| 776 | 0 | |0 124725554 |t Gradient flows |o in metric spaces and in the space of probability measures |f Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré |e 2nd edition |d 2008 |c Basel |n Birkhäuser |p 1 vol. (VII-334 p.) |s Lectures in mathematics ETH Zürich |z 978-3-7643-8721-1 | |
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