Boundary optimal control for quasistatic bilateral frictional contact problems

We consider a mathematical model describing the quasistatic process of bilateral contact with friction between an elastic body and a rigid foundation. Our goal is to study a related optimal control problem which allows us to obtain a desired field of displacements on the contact boundary, by acting with a control on another part of the boundary of the body. Using penalization and regularization techniques, we derive the necessary conditions of optimality.