Optimal design versus maximal Monge-Kantorovich metrics (Q2113545)

The paper is motivated by the connexion between the classical elastic compliance problem and the Monge transport. Some extensions are given and adaptations to some problems in optimal design of elastic structures, in particular to the optimal pre-stressed membrane problem. The investigation makes use of variational techniques, methods of convex analysis and theory of monotone maps. Some numerical simulations are also given.