TheN-membranes problem

We study the equilibrium position ofN elastic membranes attached to rigid supports and submitted to the action of forces. They are constrained because they cannot pass through each other. As in the case of the obstacle problem, the solution fails to beC ² and thus fails to be classical, so we provide some new regularity results in different larger spaces using an iterative penalization technique.On leave from Departement de Mathematiques, Universite de Metz, Ile du Saulcy, 57045 Metz-Cedex, FranceOn leave from Dipartamento di Matematica, Universita di Pisa, 56100 Pisa, Italy