# Second-order Sufficient Optimality Conditions for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions

## Inst. Mathematik

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 diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in a $L^s$-neighborhood whereby the underlying analysis allows to use weaker norms than $L^\infty$.