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

WIAS - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany; cmeyer@math.tu-berlin.de

Received: 27 April 2005
Revised: 2 May 2006

Abstract

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 an L^s-neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than .