On the solvability of a variational inequality problem and application to a problem of two membranes

Abstract

The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u = (u1, u2) ∈ K such that for all v = (v1, v2) ∈ K, ∫Ω∇u1∇(v1 − u1)+∫Ω∇u2∇(v2 − u2) + (f, v − u) ≥ 0 as a system of independent equations, where f belongs to L2(Ω) × L2(Ω) and .