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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 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.
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 meas
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 tw
This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constr
This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at the Fields Institute which
This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this be