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 pro...
Analysis in singular spaces is becoming an increasingly important area of research, with motivation coming from Calculus of Variations, PDEs, Geometric Analysis, Metric Geometry and Probability Theory, just to mention a few areas. In all these fields, the role of measure theory is crucial and an appropriate understanding of the interaction between the appropriate measure-theoretic framework and the objects under investigation is important to a successful research.
The aim of this book, which gathers contributions from leading specialists with different backgrounds, is that of creating...
Analysis in singular spaces is becoming an increasingly important area of research, with motivation coming from Calculus of Variations, PDEs, Geome...
