Free access
Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 581 - 600
DOI http://dx.doi.org/10.1051/cocv/2009010
Published online 02 July 2009
  1. J.-J. Alibert and J.-P. Raymond, Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. Numer. Funct. Anal. Optim. 3-4 (1997) 235–250. [CrossRef] [MathSciNet]
  2. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31 (1993) 993–1006. [CrossRef] [MathSciNet]
  3. E. Casas, Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. ESAIM: COCV 8 (2002) 345–374. [CrossRef] [EDP Sciences]
  4. E. Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints. ESAIM: COCV 14 (2008) 575–589. [CrossRef] [EDP Sciences]
  5. E. Casas and M. Mateos, Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J. Control Optim. 40 (2002) 1431–1454. [CrossRef] [MathSciNet]
  6. E. Casas and F. Tröltzsch, Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations. App. Math. Optim. 39 (1999) 211–227. [CrossRef]
  7. E. Casas, J.-P. Raymond and H. Zidani, Optimal control problems governed by semilinear elliptic equations with integral control constraints and pointwise state constraints, in International Conference on Control and Estimations of Distributed Parameter Systems, Vorau, Austria, 1996, W. Desch, F. Kappel and K. Kunisch Eds., Int. Series Num. Analysis, Birkhäuser-Verlag, Basel (1998) 89–102.
  8. E. Casas, F. Tröltzsch and A. Unger, Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations. SIAM J. Control Optim. 38 (2000) 1369–1391. [CrossRef] [MathSciNet]
  9. E. Casas, J. de los Reyes and F. Tröltzsch, Sufficient second order optimality conditions for semilinear control problems with pointwise state constraints. SIAM J. Optim. 19 (2008) 616–643. [CrossRef] [MathSciNet]
  10. M. Deckelnick and M. Hinze, Convergence of a finite element approximation to a state-constrained elliptic control problem. SIAM J. Numer. Anal. 45 (2007) 1937–1953. [CrossRef] [MathSciNet]
  11. M. Deckelnick and M. Hinze, Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations, in Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007, Graz, Austria, K. Kunisch, G. Of and O. Steinbach Eds., Springer, Heidelberg (2008) 597–604.
  12. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heidelberg-New York (1977).
  13. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston-London-Melbourne (1985).
  14. D. Jerison and C. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161–219. [CrossRef] [MathSciNet]
  15. M. Mateos, Problemas de control óptimo gobernados por ecuaciones semilineales con restricciones de tipo integral sobre el gradiente del estado. Ph.D. Thesis, University of Cantabria, Spain (2000).
  16. H. Maurer and J. Zowe, First- and second-order conditions in infinite-dimensional programming problems. Math. Programming 16 (1979) 98–110. [CrossRef] [MathSciNet]
  17. P. Merino, F. Tröltzsch and B. Vexler, Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space. ESAIM: M2AN (submitted).
  18. C. Meyer, Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints. Control Cybern. 37 (2008) 51–83.
  19. J. Saut and B. Scheurer, Sur l'unicité du problème de Cauchy et le prolongement unique pour des équations elliptiques à coefficients non localement bornés. J. Diff. Eq. 43 (1982) 28–43. [CrossRef] [MathSciNet]
  20. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [CrossRef] [MathSciNet]