On the approximation of the solution of an optimal control problem governed by an elliptic equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 13 (1979) no. 4, p. 313-328
@article{M2AN_1979__13_4_313_0,
author = {Geveci, Tunc},
title = {On the approximation of the solution of an optimal control problem governed by an elliptic equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {13},
number = {4},
year = {1979},
pages = {313-328},
zbl = {0426.65067},
mrnumber = {555382},
language = {en},
url = {http://www.numdam.org/item/M2AN_1979__13_4_313_0}
}

Geveci, Tunc. On the approximation of the solution of an optimal control problem governed by an elliptic equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 13 (1979) no. 4, pp. 313-328. http://www.numdam.org/item/M2AN_1979__13_4_313_0/

1. P. G. Ciarlet and P. A. Raviart, General Lagrange and Hermite interpolation in ${R}^{n}$ with applications to finite element methods, Arc. Rat. Mech. Anal., Vol. 46, 1972, pp. 177-199. | MR 336957 | Zbl 0243.41004

2. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. | MR 463994 | Zbl 0322.90046

3. R. S. Falk, Approximation of a Class of Optimal Control Problems with Order of Convergence Estimates, J. Math. Anal. Appl., Vol. 44, 1973, pp. 28-47. | MR 686788 | Zbl 0268.49036

4. R. Glowinski, Introduction to the Approximation of Elliptic Variational Inequalities, Université Paris-VI, Laboratoire Analyse numérique, Vol. 189, Paris, 1976.

5. P. Grisvard, Behaviour of Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain, SYNSPADE, 1974, B. HUBBARD, Ed., pp. 207-274, Academic Press, New York, 1976. | MR 466912 | Zbl 0361.35022

6. W. W. Hager and K. Mitter, Lagrange Duality for Convex Control Problems, S.I.A.M. J. Control, Vol. 14, 1976, pp. 842-856. | Zbl 0336.49007

7. O. A. Ladyzhenskaya and N. N. Ural'Tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | MR 244627 | Zbl 0164.13002

8. I. Lasiecka and K. Malanowski, On Regularity of Solutions to Convex Optimal Control Problems with Control Constraints for Parabolic Systems, Control and Cybernetics, Vol. 6, 1977, pp. 57-74. | MR 467439 | Zbl 0365.49003

9. I. Lasiecka and K. Malanowski, On discrete-Time Ritz-Galerkin Approximation of Control Constrained Optimal Control Problems for Parabolic Systems, Control and Cybernetics, Vol. 7, 1978, pp. 21-36. | MR 484630 | Zbl 0459.49022

10. A. Lewy and G. Stampacchia, On the Regularity of the Solution of a Variational Inequality, Comm. Pure Appl. Math., Vol. 22, 1969, pp. 153-188. | MR 247551 | Zbl 0167.11501

11. J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971. | MR 271512 | Zbl 0203.09001

12. J. Mossino, An Application of Duality to Distributed Optimal Control Problems with Constraints on the Control and the State, J. Math. Anal. Appl., Vol. 50, 1975, pp. 223-242. | MR 385670 | Zbl 0304.49003

13. M. M. Moussaoui, Régularité de la solution d'un problème à dérivée oblique, C. R. Acad. Sc, Paris, Vol. 279, série A, 1974, pp. 869-872. | MR 358062 | Zbl 0293.35014

14. J. T. Oden and N. N. Reddy, An Introduction to the Mathematical Theory of Finite Elements, Wiley-Interscience, New York, 1976. | MR 461950 | Zbl 0336.35001

15. T. Rockafellar, State Constraints in Convex Control Problems of Bolza, S.I.A.M. J. Control, Vol. 10, 1972, pp. 691-715. | MR 324505 | Zbl 0224.49003

16. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Vol. 15, 1968, pp. 189-258. | Numdam | MR 192177 | Zbl 0151.15401