Geodesic
Characterization of optimal shapes and masses through Monge-Kantorovich equation
Journal of the European Mathematical Society, Tome 3 (2001) no. 2, pp. 139-168.

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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.
DOI : 10.1007/s100970000027
Classification : 49-XX, 28-XX, 90-XX, 00-XX
Keywords: 
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     author = {Guy Bouchitt\'e and Giuseppe Buttazzo},
     title = {Characterization of optimal shapes and masses through {Monge-Kantorovich} equation},
     journal = {Journal of the European Mathematical Society},
     pages = {139--168},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2001},
     doi = {10.1007/s100970000027},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970000027/}
}
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Guy Bouchitté; Giuseppe Buttazzo. Characterization of optimal shapes and masses through Monge-Kantorovich equation. Journal of the European Mathematical Society, Tome 3 (2001) no. 2, pp. 139-168. doi : 10.1007/s100970000027. http://geodesic.mathdoc.fr/articles/10.1007/s100970000027/

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