JournalsjemsVol. 3 , No. 2DOI 10.1007/s100970000027

Characterization of optimal shapes and masses through Monge-Kantorovich equation

  • Guy Bouchitté

    Université de Toulon et du Var, La Garde, France
  • Giuseppe Buttazzo

    Università di Pisa, Italy
Characterization of optimal shapes and masses through Monge-Kantorovich equation cover

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.