Gradient Flows in Metric Spaces and in the Space of Probability Measures /

• Κύριοι συγγραφείς: Ambrosio, Luigi (Συγγραφέας), Gigli, Nicola (Συγγραφέας), Savaré, Giuseppe (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2008.
• Έκδοση: Second Edition.
• Σειρά: Lectures in Mathematics ETH Zürich
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Differential geometry.; Probabilities.; Analysis.; Measure and Integration.; Differential Geometry.; Probability Theory and Stochastic Processes.

Πίνακας περιεχομένων:

• 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).