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Abstract
A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove that the Lagrange multipliers belong to L p -spaces. Moreover, we show that if the initial value is good enough and boundary ∂ Ω has a property of positive geometric density, then multipliers and optimal solutions are Hölder continuous.
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