Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté; Giuseppe Buttazzo

Journal of the European Mathematical Society (2001)

  • Volume: 003, Issue: 2, page 139-168
  • ISSN: 1435-9855

Abstract

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We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

How to cite

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Bouchitté, Guy, and Buttazzo, Giuseppe. "Characterization of optimal shapes and masses through Monge-Kantorovich equation." Journal of the European Mathematical Society 003.2 (2001): 139-168. <http://eudml.org/doc/277390>.

@article{Bouchitté2001,
abstract = {We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.},
author = {Bouchitté, Guy, Buttazzo, Giuseppe},
journal = {Journal of the European Mathematical Society},
keywords = {Monge-Kantorovich equation; optimal distribution of masses; scalar state functions; transport problem; optimal shape; optimal mass distribution; Monge-Kantorovich equation; energy minimization},
language = {eng},
number = {2},
pages = {139-168},
publisher = {European Mathematical Society Publishing House},
title = {Characterization of optimal shapes and masses through Monge-Kantorovich equation},
url = {http://eudml.org/doc/277390},
volume = {003},
year = {2001},
}

TY - JOUR
AU - Bouchitté, Guy
AU - Buttazzo, Giuseppe
TI - Characterization of optimal shapes and masses through Monge-Kantorovich equation
JO - Journal of the European Mathematical Society
PY - 2001
PB - European Mathematical Society Publishing House
VL - 003
IS - 2
SP - 139
EP - 168
AB - We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.
LA - eng
KW - Monge-Kantorovich equation; optimal distribution of masses; scalar state functions; transport problem; optimal shape; optimal mass distribution; Monge-Kantorovich equation; energy minimization
UR - http://eudml.org/doc/277390
ER -

Citations in EuDML Documents

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  1. Aldo Pratelli, How to show that some rays are maximal transport rays in Monge Problem
  2. Luigi De Pascale, Aldo Pratelli, Sharp summability for Monge transport density via interpolation
  3. Yann Brenier, Marjolaine Puel, Optimal multiphase transportation with prescribed momentum
  4. Luigi De Pascale, Il teorema di Morse-Sard in spazi di Sobolev Problemi di trasporto ottimale e applicazioni
  5. Luigi De Pascale, Aldo Pratelli, Sharp summability for Monge Transport density Interpolation
  6. Yann Brenier, Marjolaine Puel, Optimal Multiphase Transportation with prescribed momentum
  7. Luca Granieri, Metric currents and geometry of Wasserstein spaces
  8. Alessio Brancolini, Giuseppe Buttazzo, Optimal networks for mass transportation problems
  9. Giuseppe Buttazzo, Eugene Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem
  10. Alessio Brancolini, Giuseppe Buttazzo, Optimal networks for mass transportation problems

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