Theses (Scuola Normale Superiore)
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Variational Problems in Transport Theory with Mass Concentration

Authors: Santambrogio, Filippo

  • Deals in a unified manner with several problems where different concentration effects are considered
  • Places emphasis on modeling issues
  • Considers both existence results and necessary optimality conditions for variational problems, arriving at the identification of explicit solutions when possible
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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.

Reviews

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)

Buy this book

Softcover 18,72 €
price for Spain (gross)

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Bibliographic Information

Bibliographic Information
Book Title
Variational Problems in Transport Theory with Mass Concentration
Authors
Series Title
Theses (Scuola Normale Superiore)
Series Volume
4
Copyright
2007
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
Softcover ISBN
978-88-7642-312-3
Series ISSN
2239-1460
Edition Number
1
Number of Pages
XXXII, 198
Topics