  In this paper we study we study a Dirichlet optimal control prob- lem
associated with a linear elliptic equation the coefficients of which we take as
controls in the class of integrable functions. The characteristic feature of
this control object is the fact that the skew-symmetric part of matrix-valued
control A(x) belongs to L2-space (rather than Linfinty). In spite of the fact
that the equations of this type can exhibit non-uniqueness of weak solutions,
the corresponding OCP, under rather general assumptions on the class of
admissi- ble controls, is well-posed and admits a nonempty set of solutions
[9]. However, the optimal solutions to such problem may have a singular
character. We show that some of optimal solutions can be attainable by
solutions of special optimal control problems in perforated domains with
fictitious boundary controls on the holes.

Optimization and Control;Analysis of PDEs