Luigi Ambrosio: Gradient Flows | Taschenbuch

Cover: 9783764387211 | Gradient Flows | Luigi Ambrosio (u. a.) | Taschenbuch | ix | Englisch

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Beschreibung

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. The book originates from lectures by L. Ambrosio at the ETH Zürich in Fall 2001. It contains new results that have never appeared elsewhere. The book has been substantially extended and revised in cooperation with the co-authors. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Über den Autor

Prof. Luigi Ambrosio is a Professor of Mathematical Analysis, a former student of the Scuola Normale Superiore and presently its Rector. His research interests include calculus of variations, geometric measure theory, optimal transport and analysis in metric spaces. For his scientific achievements, he has been awarded several prizes, in particular the Fermat prize in 2003, the Balzan Prize in 2019, the Riemann Prize in 2023 and the Nemmers Prize in 2024.

Dr. Elia Bruè is an Associate Professor at Bocconi University, Milan, Italy. He earned his PhD from the Scuola Normale Superiore in 2020. His research interests lie in the fields of Geometric Analysis and Partial Differential Equations, with a focus on Ricci curvature, metric geometry, incompressible fluid mechanics, and passive scalars with rough velocity fields.

Dr. Daniele Semola is an Assistant Professor at the University of Vienna. He was a student in Mathematics at the Scuola Normale Superiore, where he earned his PhD degree in 2020. His research interests lie at the interface between geometric analysis and analysis on metric spaces, mainly with a focus on lower curvature bounds.

Zusammenfassung

Inhaltsverzeichnis

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).

Details

Erscheinungsjahr:	2008
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 334 S.
ISBN-13:	9783764387211
ISBN-10:	3764387211
Sprache:	Englisch
Herstellernummer:	12176106
Einband:	Kartoniert / Broschiert
Autor:	Ambrosio, Luigi Gigli, Nicola Savare, Giuseppe
Auflage:	Second Edition 2008
Hersteller:	Birkhäuser Springer Basel AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	240 x 168 x 19 mm
Von/Mit:	Luigi Ambrosio (u. a.)
Erscheinungsdatum:	13.03.2008
Gewicht:	0,585 kg