Gangbo (Georgia Institute of Technology, Atlanta), H.K. Kim (New York U.), and T. Pacini (Scuola normale Superiiore, Pisa, Italy) present the foundation for a new framework for defining and studying Hamiltonian partial differential equations. Over the past decade, they explain, it has become clear that the Wasserstein space provides a very useful space of weak solutions for those equations in which total mass is preserved. The theory of Wasserstein spaces is founded on optimal transport and calculus of variation, which provide a toolbox that can be expected to be uniformly useful throughout the theory, thus offering a unified theory for studying the equations. There is no index. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)