Existence of a Solution to a Stationary Quasi-Variational Inequality in a Multi-Connected Domain

We consider a stationary quasi-variational inequality in a multi-connected domain and show the existence of a solution to the inequality. The problem is related to the Bean critical-state model in type II superconductors. Mathematically, we are concerned with a quasi-variational inequality containing a p-curl inequality with a curl constraint by a function of the solution.