Descrizione

The thesis mainly deals with variational problems involving optimal transportation of probability measures, in competition with concentration effects. First, some problems where measures have to be selected minimizing transport costs between them but satisfying some concentration criteria are presented in the first chapters, with possible applications mainly to urban planning (where the concentrated measures stand for services in the city and the diffuse ones for population). A second part of the thesis is devoted to optimization problems where the concentration or diffusion phenomena occur directly at the level of the transportation structure: for instance in most communication networks, as well as in river basins and blood vessels joint transportation is favoured, while some models for traffic congestion or compressible fluid mechanics give rise to problems where spread configurations are preferred.