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Gradient Flows in Metric Spaces and in the Space of Probability Measures by Luigi Ambrosio

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Published by Birkhäuser Basel in Basel .
Written in English

Subjects:

  • Global differential geometry,
  • Mathematics,
  • Distribution (Probability theory)

Book details:

Edition Notes

Statementby Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré ; edited by Michael Struwe
SeriesLectures in Mathematics ETH Zürich
ContributionsGigli, Nicola, Savaré, Giuseppe, Struwe, Michael, 1955-, SpringerLink (Online service)
The Physical Object
Format[electronic resource] :
ID Numbers
Open LibraryOL25564714M
ISBN 109783764387211, 9783764387228

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‎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 and contains new results. 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 of probability measures on p a separable. Gradient Flows In Metric Spaces and in the Space of Probability Measures. Authors: Ambrosio, L., Gigli, Nicola, Savare, Giuseppe Free PreviewBrand: Birkhäuser Basel. Gradient Flow helps you stay ahead of the latest technology trends and tools with in-depth coverage, analysis and insights. See the latest on data, technology and business, with a .

  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 of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein.   This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of . 3 Gradient Flow in Metric Spaces Generalization of Basic Concepts Generalization of Gradient Flow to Metric Spaces 4 Gradient Flows on Wasserstein Spaces Recap. of Optimal Transport Problems The Wasserstein Space Gradient Flows on W 2(); ˆRn Numerical methods from the JKO scheme 5 Application 6 My Remarks 7 Appendix Chang Liu (THU) Gradient. The movement of blood from the heart throughout the arteries is due to a _____ gradient. Concentration. Charged particles, like Na⁺ and Cl⁻, flow down _____ gradients when ion channels are open. Thermal. Heat flows from warm areas to cool areas down a _____ gradient. OTHER SETS BY THIS CREATOR. Hist Final Exam.

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. Particular emphasis is given to the convergence of the implicit time discretization method and to. Gradient Flows in Metric Spaces and in the Space of Probability Measures. Authors (view affiliations) About this book. Keywords. Gradient flows Hilbert space Maxima Maximum Measure theory Metric spaces Probability measures Riemannian structures calculus differential equation measure.   Studying the gradient flow in lieu of the gradient descent recursions comes with pros and cons. Simplified gradient flow has no step-size, so all the traditional annoying issues regarding the choice of step-size, with line-search, constant, decreasing or with a .   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.