Résumé en anglais

In open pit mining, one must dig a pit, that is, excavate the upperlayers of ground before reaching the ore. The walls of the pit must satisfysome mechanical constraints, in order not to collapse. The question thenarises how to mine the ore optimally, that is, how to Önd the optimalpit. We set up the problem in a continuous (as opposed to discrete)framework, and we show, under weak assumptions, the existence of anoptimum pit. For this, we formulate an optimal transportation problem,where the criterion is lower semi-continuous and is allowed to take thevalue+1. We show that this transportation problem is a strong dualto the optimum pit problem, and also yields optimality (complementarityslackness) conditions.