Control problem on a rough circular domain and homogenization

Abstract

This paper is concerned with the asymptotic analysis of optimal control problems posed on a rough circular domain. The domain has two parts, namely a fixed outer part and an oscillating inner part. The period of the oscillation is of order ε > 0, a small parameter which approaches zero and the amplitude of the oscillation is fixed. We pose a periodic control on the oscillating part of the domain and study the homogenization of this problem using an unfolding operator suitably defined for this domain. One of the novelties of this paper is that we use the unfolding operator to characterize the optimal control in the non-homogenized level.