Relaxation of a weakly discontinuous functional depending on one control function

Abstract

The paper considers an optimal control problem of the type

where the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h ₁ or h ₂. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

Key words:

• optimal control
• elliptic system
• weakly discontinuous functional
• relaxation