M. B. Abrahamse, Toeplitz Operators in Multiply Connected Regions, American Journal of Mathematics, vol.96, issue.2, pp.261-297, 1974.
DOI : 10.2307/2373633

G. Alessandrini, D. Piero, L. Rondi, and L. , Stable determination of corrosion by a single electrostatic boundary measurement, Inverse Problems, vol.19, issue.4, pp.973-984, 2003.
DOI : 10.1088/0266-5611/19/4/312

D. Alpay, L. Baratchart, and J. Leblond, Some extremal problems linked with indentification from partial frequency data, Lecture Notes in Control and Inform. Sci, vol.185, pp.563-573, 1993.
DOI : 10.1007/BFb0115054

B. Atfeh, L. Baratchart, J. Leblond, and J. R. Partington, Bounded Extremal and Cauchy???Laplace Problems on??the??Sphere and Shell, Journal of Fourier Analysis and Applications, vol.11, issue.2, 2008.
DOI : 10.1007/s00041-009-9110-0
URL : https://hal.archives-ouvertes.fr/inria-00272203

J. A. Ball and K. F. Clancey, Reproducing kernels for Hardy spaces on multiply connected domains, Integral Equations and Operator Theory, vol.13, issue.1, pp.35-57, 1996.
DOI : 10.1007/BF01192041

L. Baratchart and J. Leblond, Identification harmonique et traces des classes de Hardy sur un arc de cercle, Proc. Conf. 60th birthday of Prof. Jean Céa, pp.17-29, 1992.

K. Bryan and M. Vogelius, Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling, Quarterly of Applied Mathematics, vol.60, issue.4, pp.675-694, 2002.
DOI : 10.1090/qam/1939006

S. Chaabane, C. Elhechmi, and M. Jaoua, A stable recovery algorithm for the Robin inverse problem, Mathematics and Computers in Simulation, vol.11, issue.1, pp.33-57, 2003.

S. Chaabane, C. Elhechmi, and M. Jaoua, Error estimates in smoothing noisy data using cubic B-splines, Comptes Rendus Mathematique, vol.346, issue.1-2, 2008.
DOI : 10.1016/j.crma.2007.10.045

S. Chaabane, I. Fellah, M. Jaoua, and J. Leblond, Logarithmic stability estimates for a Robin coefficient in two-dimensional Laplace inverse problems, Inverse Problems, vol.20, issue.1, pp.47-59, 2004.
DOI : 10.1088/0266-5611/20/1/003

S. Chaabane and M. Jaoua, Identification of Robin coefficients by the means of boundary measurements, Inverse Problems, vol.15, issue.6, pp.1425-1438, 1999.
DOI : 10.1088/0266-5611/15/6/303

S. Chaabane, M. Jaoua, and J. Leblond, Parameter identification for Laplace equation and approximation in Hardy classes, Journal of Inverse and Ill-posed Problems, vol.11, issue.1, pp.33-57, 2003.
DOI : 10.1515/156939403322004928
URL : https://hal.archives-ouvertes.fr/inria-00072292

I. Chalendar, J. Leblond, and J. R. Partington, Approximation problems in some holomorphic spaces, with applications " , Systems, Approximation, Singular Integral Operators and Related Topics, Proceedings of IWOTA 2000, pp.143-168, 2001.

I. Chalendar and J. R. Partington, Approximation problems and representations of Hardy spaces in circular domains, Studia Math, vol.136, pp.255-269, 1999.

D. Fasino and G. Inglese, An inverse Robin problem for Laplace's equation: theoretical results and numerical methods, Inverse Problems, vol.15, issue.1, pp.41-48, 1999.
DOI : 10.1088/0266-5611/15/1/008

D. Fasino and G. Inglese, Discrete methods in the study of an inverse problem for Laplace's equation, IMA Journal of Numerical Analysis, vol.19, issue.1, pp.105-118, 1999.
DOI : 10.1093/imanum/19.1.105

G. M. Goluzin, Geometric theory of functions of a complex variable, 1969.

B. Jacob, J. Leblond, J. Marmorat, and J. R. Partington, A constrained approximation problem arising in parameter identification, Linear Algebra and its Applications, vol.351, issue.352, pp.351-352, 2002.
DOI : 10.1016/S0024-3795(01)00445-1
URL : https://hal.archives-ouvertes.fr/hal-00504824

S. I. Kabanikhin and A. L. Karchevsky, Optimizational method for solving the Cauchy problem for an elliptic equation, Journal of Inverse and Ill-Posed Problems, vol.3, issue.1, pp.21-26, 1995.
DOI : 10.1515/jiip.1995.3.1.21

P. Kaup and F. Santosa, Nondestructive evaluation of corrosion damage using electrostatic measurements, Journal of Nondestructive Evaluation, vol.53, issue.1, pp.127-136, 1995.
DOI : 10.1007/BF01183118

P. Kaup, F. Santosa, and M. Vogelius, Method for imaging corrosion damage in thin plates from electrostatic data, Inverse Problems, vol.12, issue.3, pp.279-293, 1996.
DOI : 10.1088/0266-5611/12/3/008

O. Kavian and . Vogelius, On the existence and " blow-up " of solutions a two dimensional nonlinear boundary value problem arising in corrosion modeling, Proc. Roy. Soc. Edinburgh, 133A, pp.119-149, 2003.

J. Kiefer, Sequential minimax search for a maximum, Proceedings of the American Mathematical Society, pp.502-506, 1953.

M. V. Klibanov and F. Santosa, A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace???s Equation, SIAM Journal on Applied Mathematics, vol.51, issue.6, pp.1653-1675, 1995.
DOI : 10.1137/0151085

R. V. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography, Communications on Pure and Applied Mathematics, vol.34, issue.6, pp.745-777, 1987.
DOI : 10.1002/cpa.3160400605

V. A. Kozlov, V. G. Maz-'ya, and A. V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations, Comput. math. Phys, vol.31, pp.45-52, 1991.

J. Leblond, M. Mahjoub, and J. R. Partington, Analytic extensions and Cauchytype inverse problems on annular domains: stability results, J. Inv. Ill. P. Problems, vol.16, pp.189-204, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00070601

P. Ch, Boundary Behaviour of Conformal Maps, 1991.

W. Rudin, Analytic functions of class H p, Trans. Amer. Math. Soc, vol.78, pp.46-66, 1955.

F. Santosa, M. Vogelius, and J. Xu, An effective nonlinear boundary condition for a corroding surface. Identification of the damage based on steady state electric data, Zeitschrift fur Angewandte Mathematik und Physik, pp.656-679, 1998.
DOI : 10.1007/s000000050114

M. P. Smith, The Spectral Theory of Toeplitz Operators Applied to Approximation Problems in Hilbert Spaces, Constructive Approximation, vol.22, issue.1, pp.47-65, 2005.
DOI : 10.1007/s00365-004-0591-4

N. Torkhani, ContributionàContribution`Contributionà l'identification fréquentielle robuste des systèmes dynamiques linéaires, 1995.

M. Vogelius and J. M. Xu, A nonlinear elliptic boundary value problem related to corrosion modeling, Quarterly of Applied Mathematics, vol.56, issue.3, pp.479-505, 1998.
DOI : 10.1090/qam/1637048