Journal of the European Mathematical Society
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Characterization of optimal shapes and masses through Monge-Kantorovich equationGuy Bouchitté and Giuseppe Buttazzo (1) Département de Mathématiques, Université de Toulon et du Var, BP 132, 83957, La Garde CEDEX, France
(2) Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
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.
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Bouchitté Guy, Buttazzo Giuseppe: Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001), 139-168. doi: 10.1007/s100970000027