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

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 diffusegray 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 an L-neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L∞. Mathematics Subject Classification. 49K20, 35J65, 80M50. Received April 27, 2005. Revised May 2, 2006. Published online July 20, 2007.