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We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diuse-gra y conductive-radiative heat transfer. After stating rst-order necessary conditions, second- order sucien t conditions are derived that account for strongly active sets. These conditions ensure local optimality in an L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L 1 .

Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions