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Variational Problems in Transport Theory with Mass Concentration

  • Book
  • Dec 2007

Overview

Authors:
  1. Filippo Santambrogio
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  • 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)

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Keywords

  • Wasserstein space
  • optimal transport
  • traffic congestion
  • transport problem

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)

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

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