On necessary optimality conditions for optimal control problems governed by elliptic systems
Uldis Raitums, W. H. Schmidt · Optimization · 2005
The article considers an optimal control problem for the linear elliptic system div for the case where the coefficient matrix A plays the role of control and belongs to a nonconvex set and the cost functional is a quadratic form with respect to . By transforming the original problem to a more suitable one and by using ideas from the homogenization theory a necessary optimality condition is derived.