Luigi Ambrosio, Nicola Gigli, Giuseppe Savare

Gradient Flows

In Metric Spaces and in the Space of Probability Measures

• Broschiertes Buch

Produktbeschreibung

This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. The book originates from lectures by L. Ambrosio at the ETH Zürich in Fall 2001 and contains new results.

Produktdetails

• Lectures in Mathematics
• Verlag: Birkhäuser / Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 12176106, 978-3-7643-8721-1
• 2nd ed.
• Seitenzahl: 348
• Erscheinungstermin: 13. März 2008
• Englisch
• Abmessung: 240mm x 168mm x 19mm
• Gewicht: 604g
• ISBN-13: 9783764387211
• ISBN-10: 3764387211
• Artikelnr.: 23275070

Inhaltsangabe

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).