Relaxation of a weakly discontinuous functional depending on one control function

Abstract

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

Keywords

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