On necessary optimality conditions for optimal control problems governed by elliptic systems

Abstract

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.

Keywords:

• Optimal control
• Elliptic system
• Necessary optimality condition
• Laminate variation
• Mathematical Subject Classifications 1991: 49K20
• 93C20