The nonlinear problem of two membranes

Abstract

The problem of finding the position of two membranes, one constrained by the other, attached to rigid supports, subjected to external forces, is considered. It is proved existence of solution, if we assume a compatibility condition relating the mean curvature of the boundary of the set where the problem is defined and the given data. It is also proved the W2,p regularity of the solution, for 1 ≤ p < +∞.

Keywords

• variational inequalities
• partial differential equations
• minimal surfaces operator