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Variational Problems in Transport Theory with Mass Concentration

Filippo Santambrogio (Autor)

Buch | Softcover

198 Seiten

2007
Scuola Normale Superiore (Verlag)
9788876423123 (ISBN)

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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.

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.

Erscheint lt. Verlag	13.12.2007
Reihe/Serie	Publications of the Scuola Normale Superiore ; 4
Reihe/Serie	Theses (Scuola Normale Superiore)
Zusatzinfo	XXXII, 198 p.
Verlagsort	Pisa
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-13	9788876423123 / 9788876423123
Zustand	Neuware