Abstract
This paper deals with optimal control problems governed by semilinear parabolic equations in presence of pointwise constraints on the state variable. We obtain necessary optimality conditions in which the adjoint state satisfies a parabolic equation with measures as source terms. We prove new existence and regularity results for solutions of such equations. For simplicity we only consider the case of a boundary control, but the results can be extended to problems with a control in the initial condition and a distributed control.
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