ABSTRACT
The aim of this paper is to present some existence results for an optimal shape design problem for systems described by hemivariational inequalities of elliptic and parabolic type. These problems may be formulated as control problems in which hemivariational inequalities appear as state equations and the role of controls is played by sets from a family of admissible shapes. The cost functional to be minimized is of general (not necessary integral) form. Such control problems governed by variational inequalities, of both elliptic and parabolic type, were studied by Liu and Rubio in [7] and [8], where the applications of these problems to the so called electrochemical machining are given.
