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, $1<p<\infty$, 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.