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

 Source file is available as : Postscript Document Portable Document Format (PDF)

Author(s) : Christian Meyer

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 13-2005

MSC 2000

49K20 Problems involving partial differential equations
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE

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 a $L^s$-neighborhood whereby the underlying analysis allows to use weaker norms than $L^\infty$.

Keywords : Optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions

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