Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 581-600.

Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.

DOI: 10.1051/cocv/2009010
Classification: 49J20, 49K20, 35J65
Keywords: optimal control, pointwise state constraints, first and second order optimality conditions, Lagrange multipliers, Borel measures
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     title = {Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems},
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Casas, Eduardo; Tröltzsch, Fredi. Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 581-600. doi : 10.1051/cocv/2009010. http://archive.numdam.org/articles/10.1051/cocv/2009010/

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