الصفحة 1
الصفحة 1
Gradient Flows : in Metric Spaces and in the Space of Probability Measures ; 2nd ed.
Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.
Gradient Flows : In Metric Spaces and in the Space of Probability Measures ; 1st ed.
This book is devoted to a theory of gradient flows in spaces which are not nec- sarily endowed with a natural linear or differentiable structure. It is made of two parts, the first one concerning gradient flows in metric spaces and the second one 2 1 devoted to gradient flows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Differential Equations, Measure Theory and Probability.
Calculus of variations and nonlinear partial differential equations : With a historical overview by Elvira Mascolo : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
