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, 2005.
• Σειρά: Lectures in Mathematics ETH Zürich
• Θέματα: Mathematics.; Measure theory.; Differential geometry.; Probabilities.; Measure and Integration.; Differential Geometry.; Probability Theory and Stochastic Processes.

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 1 devoted to gradient ?ows in the L -Wasserstein space...

Πίνακας περιεχομένων:

• 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
• Notation
• 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 Pp(X) and the Continuity Equation
• Convex Functionals in Pp(X)
• Metric Slope and Subdifferential Calculus in Pp(X)
• Gradient Flows and Curves of Maximal Slope in Pp(X).