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All issues Volume 16 / No 3 (July-September 2010) ESAIM: COCV, 16 3 (2010) 581-600 References
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Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 581 - 600
DOI https://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. [Google Scholar]
  2. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31 (1993) 993–1006. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  12. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heidelberg-New York (1977). [Google Scholar]
  13. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston-London-Melbourne (1985). [Google Scholar]
  14. D. Jerison and C. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161–219. [CrossRef] [MathSciNet] [Google Scholar]
  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). [Google Scholar]
  16. H. Maurer and J. Zowe, First- and second-order conditions in infinite-dimensional programming problems. Math. Programming 16 (1979) 98–110. [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]

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