Document ESAIM: COCV, Vol. 13, N°4, pp. 750-775
DOI: 10.1051/cocv:2007028
Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions
Christian MeyerWIAS - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany; cmeyer@math.tu-berlin.de
(Received April 27, 2005. Revised May 2, 2006. Published online July 20, 2007.)
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
Ls-neighborhood of a reference function
whereby the underlying analysis allows to use
weaker norms than 
.
Mathematics Subject Classification. 49K20, 35J65, 80M50
Key words: Optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions
© EDP Sciences, SMAI 2007