Journal of the European Mathematical Society


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Volume 3, Issue 2, 2001, pp. 139–168
DOI: 10.1007/s100970000027

Published online: 2001-06-30

Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté[1] and Giuseppe Buttazzo[2]

(1) Université de Toulon et du Var, La Garde, France
(2) Università di 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