Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009010 Published online 02 July 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009010

Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas¹ and Fredi Tröltzsch<sup>2

1</sup>  Dpt. Matemática Aplicada y Ciencias de la Computación, E.T.S.I.I. y T., Universidad de Cantabria, Av. Los Castros s/n, 39005 Santander, Spain. eduardo.casas@unican.es
²  Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany. troeltzsch@math.tu-berlin.de

Received July 20, 2008. Revised February 24, 2009. Published online July 2nd, 2009.

Abstract
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.

Mathematics Subject Classification. 49J20, 49K20, 35J65

Key words: Optimal control, pointwise state constraints, first and second order optimality conditions, Lagrange multipliers, Borel measures


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