Optimal shape design and unilateral boundary value problems. I.

Abstract

In the first part we give a general existence theorem and a regularization method for an optimal control problem where the control is a domain in R″ and where the system is governed by a state relation which includes differential equations as well as inequalities. In the second part applications for optimal shape design problems governed by the Dirichlet‐Signorini boundary value problem are presented. Several numerical examples are included.