The N-membranes problem for quasilinear degenerate systems

Abstract

We study the regularity of the solution of the variational inequality for the problem of N-membranes in equilibrium with a degenerate operator of p-Laplacian type, 1 < p < ∞, for which we obtain the corresponding Lewy-Stampacchia inequalities. By considering the problem as a system coupled through the characteristic functions of the sets where at least two membranes are in contact, we analyze the stability of the coincidence sets.