Authors:
Deals in a unified manner with several problems where different concentration effects are considered
Key points of the book are modelling issues
For variational problems both existence results and necessary optimality conditions are considered, arriving at the identification of explicit solutions when possible
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 4)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
About this book
The book mainly deals with variational problems involving optimal transportation of probability measures, in competition with concentration effects. First, some problems are presented where measures have to be selected minimizing transport costs between them but satisfying some concentration criteria, with possible applications mainly to urban planning (where the concentrated measures stand for services in the city and the diffuse ones for population). The second part of the book is devoted to optimization problems where the concentration or diffusion phenomena occurs 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 raise to problems where spread configurations are preferred.
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Bibliographic Information
Book Title: Variational Problems in Transport Theory with Mass Concentration
Authors: Filippo Santambrogio
Series Title: Publications of the Scuola Normale Superiore
Publisher: Edizioni della Normale Pisa
Copyright Information: Edizioni della Normale 2007
Softcover ISBN: 978-88-7642-312-3Due: 13 December 2007
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Number of Pages: XXXII, 198
Topics: Calculus of Variations and Optimal Control; Optimization