Homogenization of Some Problems with Rapidly Oscillating Constraints

Homogenization theorems are proved for the problem of minimization of a quadratic integral functional on a set of admissible functions satisfying rapidly oscillating periodic constraints on the boundary of a perforated domain. At each point of the perforation surface, the trace of any admissible function belongs to a given segment of the real axis, and this segment periodically varies along the boundary. According to the structure of this field of segments on the boundary, we characterize the asymptotic behavior of the solutions (minimizers) as the period of the structure tends to zero.