From the reviews: The book deals with optimal transport problems where concentration phenomena, such as concentration of the marginal measures or along the transport itself, occur. The content of the volume is divided into 10 chapters preceded by an Introduction outlining the main results obtained by the author. the text will be of real interest for applied mathematicians. (Adriana-Ioana Lefter, Memoirs of the Scientific Sections, 2009)

This book examines variational problems involving optimal transportation of probability measures, in competition with concentration effects. It presents some problems where measures have to be selected minimizing transport costs between them, but satisfying some concentration criteria, with possible applications to urban planning. The book also covers optimization problems where the concentration or diffusion phenomena occurs directly at the level of the transportation structure.

Preliminaries on optimal transportation.- 1. An urban planning model by local functionals.- 2. An urban planning model with traffic congestion.- 3. Transport and concentration problems with interaction.- 4. Path functionals in Wasserstein spaces.- 5. A system of PDEs from a geodesic problem in Wp.- 6. Branching transport problems and distances.- 7. Landscape function.- 8. Blow-up for optimal one-dimensional sets.- 9. Blow-up for optimal branching structures.- References.