Free access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 575 - 589
DOI http://dx.doi.org/10.1051/cocv:2007063
Published online 21 December 2007
  1. N. Arada, E. Casas and F. Tröltzsch, Error estimates for the numerical approximation of a semilinear elliptic control problem. Comput. Optim. Appl. 23 (2002) 201–229. [CrossRef] [MathSciNet]
  2. J.F. Bonnans and E. Casas, Contrôle de systèmes elliptiques semilinéaires comportant des contraintes sur l'état, in Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar 8, H. Brezis and J.-L. Lions Eds., Longman Scientific & Technical, New York (1988) 69–86.
  3. E. Casas, Pontryagin's principle for optimal control problems governed by semilinear elliptic equations, in International Conference on Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena, F. Kappel and K. Kunisch Eds., Basel, Birkhäuser, Int. Series Num. Analysis. 118 (1994) 97–114.
  4. 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]
  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 M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comp. Appl. Math. 21 (2002) 67–100.
  7. 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]
  8. E. Casas and F. Tröltzsch, Second order necessary and sufficient optimality conditions for optimization problems and applications to control theory. SIAM J. Optim. 13 (2002) 406–431. [CrossRef] [MathSciNet]
  9. 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, W. Desch, F. Kappel and K. Kunisch Eds., Basel, Birkhäuser, Int. Series Num. Analysis. 126 (1998) 89–102.
  10. 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]
  11. F.H. Clarke, A new approach to Lagrange multipliers. Math. Op. Res. 1 (1976) 165–174. [CrossRef] [MathSciNet]
  12. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston-London-Melbourne (1985).
  13. E. Hewitt and K. Stromberg, Real and abstract analysis. Springer-Verlag, Berlin-Heidelberg-New York (1965).
  14. W. Littman and G. Stampacchia and H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Normale Sup. Pisa 17 (1963) 43–77.
  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. Program. 16 (2000) 431–450.
  17. J.-P. Raymond and F. Tröltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints. Discrete Contin. Dynam. Systems 6 (1979) 98–110.
  18. S.M. Robinson, Stability theory for systems of inequalities, Part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13 (1976) 497–513. [CrossRef] [MathSciNet]
  19. J.C. 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. Differential Equations 43 (1982) 28–43. [CrossRef] [MathSciNet]