# 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

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topBouchitté, 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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- Luigi De Pascale, Aldo Pratelli, Sharp summability for Monge transport density via interpolation
- Yann Brenier, Marjolaine Puel, Optimal multiphase transportation with prescribed momentum
- Luigi De Pascale, Il teorema di Morse-Sard in spazi di Sobolev Problemi di trasporto ottimale e applicazioni
- Luigi De Pascale, Aldo Pratelli, Sharp summability for Monge Transport density Interpolation
- Yann Brenier, Marjolaine Puel, Optimal Multiphase Transportation with prescribed momentum
- Luca Granieri, Metric currents and geometry of Wasserstein spaces
- Alessio Brancolini, Giuseppe Buttazzo, Optimal networks for mass transportation problems
- Giuseppe Buttazzo, Eugene Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem
- Alessio Brancolini, Giuseppe Buttazzo, Optimal networks for mass transportation problems

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