Abstract
This paper investigates two optimal control problems in which the state equation is a quasi-linear elliptic partial differential equation. In the first problem the admissible set comprises functions with range in the interval [0,1] with prescribed integral. We show the optimal solution is unique and it is of bang-bang type. In the second problem the admissible set is a particular class of simple functions. We will show again the optimal solution is unique and derive the corresponding optimality condition.
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