R. A. Adams, Sobolev spaces, 1975.

F. Alvarez, J. Bolte, J. F. Bonnans, and F. Silva, Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems, Mathematical Programming, vol.77, issue.1, 2009.
DOI : 10.1007/s10107-011-0477-8

URL : https://hal.archives-ouvertes.fr/inria-00365540

T. Appel, A. Rösch, and G. Winkler, Optimal control in non-convex domains: a priori discretization error estimates, Calcolo, vol.44, issue.3, pp.137-158, 2007.
DOI : 10.1007/s10092-007-0133-0

N. Arada, E. Casas, and F. Tröltzsch, Error estimates for the numerical approximation of a semilinear elliptic control problem, Computational Optimization and Applications, vol.23, issue.2, pp.201-229, 2002.
DOI : 10.1023/A:1020576801966

M. Bergounioux, M. Haddou, M. Hintermüller, and K. Kunisch, A Comparison of a Moreau--Yosida-Based Active Set Strategy and Interior Point Methods for Constrained Optimal Control Problems, SIAM Journal on Optimization, vol.11, issue.2, pp.495-521, 2000.
DOI : 10.1137/S1052623498343131

URL : https://hal.archives-ouvertes.fr/hal-00022028

J. T. Betts, S. K. Eldersveld, P. D. Frank, and J. G. Lewis, An Interior-Point Algorithm for Large Scale Optimization, Large-scale PDE-constrained optimization, pp.184-198, 2001.
DOI : 10.1007/978-3-642-55508-4_11

J. F. Bonnans, Second-Order Analysis for Control Constrained Optimal Control Problems of Semilinear Elliptic Systems, Applied Mathematics and Optimization, vol.38, issue.3, pp.38-3303, 1998.
DOI : 10.1007/s002459900093

URL : https://hal.archives-ouvertes.fr/inria-00073680

J. F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems, 2000.
DOI : 10.1007/978-1-4612-1394-9

H. Brézis, Probì emes unilatéraux, J. Mathématiques pures et appliquées, vol.51, pp.1-168, 1972.

H. Brézis, Analyse Fonctionnelle, Théorie et Applications. Collection Mathématiques Appliquées pour la Ma??triseMa??trise, 1983.

E. Casas, Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems, Advances in Computational Mathematics, vol.29, issue.1-3, pp.137-153, 2007.
DOI : 10.1007/s10444-004-4142-0

E. Casas, F. Tröltzsch, and A. Unger, Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem, Zeitschrift f??r Analysis und ihre Anwendungen, vol.15, issue.3, pp.687-707, 1996.
DOI : 10.4171/ZAA/723

K. Deckelnick and M. Hinze, Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.1937-1953, 2007.
DOI : 10.1137/060652361

L. C. Evans, Partial differential equations, Amer. Math Soc. Graduate Studies in Mathematics, vol.19, 1998.

H. O. Fattorini, Infinite dimensional optimization and control theory, 1998.
DOI : 10.1017/CBO9780511574795

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 1983.

A. Haraux, How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities, Journal of the Mathematical Society of Japan, vol.29, issue.4, pp.615-631, 1977.
DOI : 10.2969/jmsj/02940615

M. Hintermüller and K. Kunisch, Path-following Methods for a Class of Constrained Minimization Problems in Function Space, SIAM Journal on Optimization, vol.17, issue.1, pp.159-187, 2006.
DOI : 10.1137/040611598

M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich, Optimization with PDE constraints, 2008.

X. Li and J. Yong, Optimal control theory for infinite dimensional systems, Birkhäuser, 1995.
DOI : 10.1007/978-1-4612-4260-4

J. Lions, Contrôle optimal de systèmes gouvernés par des equations aux dérivées partielles, 1968.

H. Maurer, Optimization techniques for solving elliptic control problems with control and state constraint. part 2: Distributed control, Computational Optimization and Applications, vol.18, issue.2, pp.141-160, 2001.
DOI : 10.1023/A:1008774521095

H. Maurer and H. D. Mittelmann, Optimization techniques for solving elliptic control problems with control and state constraint. part 1: Boundary control, Computational Optimization and Applications, vol.16, issue.1, pp.29-55, 2000.
DOI : 10.1023/A:1008725519350

F. Mignot, Contrôle dans les inéquations variationnelles, J. Functional Analysis, vol.22, pp.25-39, 1976.

P. Neittaanmaki, J. Sprekels, and D. Tiba, Optimization of elliptic systems, 2006.

A. Schiela, Barrier Methods for Optimal Control Problems with State Constraints, SIAM Journal on Optimization, vol.20, issue.2, pp.1002-1031, 2009.
DOI : 10.1137/070692789

A. Schiela and M. Weiser, Superlinear convergence of the control reduced interior point method for PDE constrained optimization, Computational Optimization and Applications, vol.4, issue.1, pp.369-393, 2008.
DOI : 10.1007/s10589-007-9057-5

J. Sokolowski, Sensitivity Analysis of Control Constrained Optimal Control Problems for Distributed Parameter Systems, SIAM Journal on Control and Optimization, vol.25, issue.6, pp.1542-1556, 1987.
DOI : 10.1137/0325085

G. Stampacchia, Le probl??me de Dirichlet pour les ??quations elliptiques du second ordre ?? coefficients discontinus, Annales de l???institut Fourier, vol.15, issue.1, pp.189-258, 1965.
DOI : 10.5802/aif.204

M. Ulbrich and S. Ulbrich, Superlinear Convergence of Affine-Scaling Interior-Point Newton Methods for Infinite-Dimensional Nonlinear Problems with Pointwise Bounds, SIAM Journal on Control and Optimization, vol.38, issue.6, pp.1938-1984, 2000.
DOI : 10.1137/S0363012997325915

M. Ulbrich and S. Ulbrich, Primal-dual interior-point methods for PDE-constrained optimization, Mathematical Programming, vol.4, issue.1, pp.435-485, 2009.
DOI : 10.1007/s10107-007-0168-7

M. Weiser, T. Gänzler, and A. Schiela, A control reduced primal interior point method for a class of control constrained optimal control problems, Computational Optimization and Applications, vol.4, issue.1, pp.127-145, 2008.
DOI : 10.1007/s10589-007-9088-y

M. Weiser and A. Schiela, Function space interior point methods for PDE constrained optimization, PAMM, vol.1, issue.1, pp.43-46, 2004.
DOI : 10.1002/pamm.200410011