Gradient Flows
In Metric Spaces and in the Space of Probability Measures
Buch in deiner Nähe kaufen
Beschreibung
Originating from lectures by L. Ambrosio at the ETH Zürich in Fall 2001 Substantially extended and revised in cooperation with the co-authors Serves as textbook and reference book on the topic Presented as much as possible in a self-contained way Containing new results that never appeared elsewhere Includes supplementary material: sn.pub/extras
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.
Autor*in
Luigi Ambrosio
Themen in »Gradient Flows«
Gradient flows Hilbert space Maxima Maximum Measure theory Metric spaces Probability measures Riemannian structures calculus differential equation measure