The N-membranes problem with Neumann boundary condition

Abstract

We consider the problem of finding the equilibrium position of N membranes constrained not to pass through each other, under prescribed volumic forces and boundary tensions. This model corresponds to solve variationally a N-system for linear second order elliptic equations with sequential constraints. We obtain interior and boundary Lewy-Stampacchia type inequalities for the respective solution and we establish the conditions for stability in measure of the interior contact zones of the membranes.