Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 750-775.

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 ${L}^{\infty }$.

DOI : https://doi.org/10.1051/cocv:2007028
Classification : 49K20,  35J65,  80M50
Mots clés : optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions
@article{COCV_2007__13_4_750_0,
author = {Meyer, Christian},
title = {Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {750--775},
publisher = {EDP-Sciences},
volume = {13},
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year = {2007},
doi = {10.1051/cocv:2007028},
zbl = {1127.49020},
mrnumber = {2351402},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007028/}
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Meyer, Christian. Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 750-775. doi : 10.1051/cocv:2007028. http://www.numdam.org/articles/10.1051/cocv:2007028/

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