Por Guy Bouchitté (Université de Toulon).

In 1997, a remarkable connection was discovered between the optimal compliance problem for the heat equation and Monge's mass transport theory, allowing solutions to be constructed using a purely geometric approach.

The aim of this talk is to present recent successful (or partially successful) attempts to extend such a connection to the vector framework of elasticity: Michell's problem, the design of a prestressed membrane, the optimal vault problem and, more recently, the optimal grillage problem.

Some long-standing open questions are also addressed.