G. Alessandrini, E. Beretta, E. Rosset, and S. Vessella, Optimal stability for inverse elliptic boundary value problems with unknown boundaries, Annali della Scuola Normale Superiore di Pisa, vol.29, issue.4, pp.755-806, 2000.

L. Bourgeois, Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation. Inverse problems, pp.413-430, 2006.

L. Bourgeois and J. Dardé, Conditional stability for ill-posed elliptic Cauchy problems : the case of Lipschitz domains (part II), 2008.
URL : https://hal.archives-ouvertes.fr/inria-00324166

A. L. Bukhgeim, Extension of Solutions of elliptic equations from discrete sets, Journal of Inverse and Ill-Posed Problems, vol.1, issue.1, pp.17-32, 1993.
DOI : 10.1515/jiip.1993.1.1.17

T. Carleman, Sur unprobì eme d'unicité pour les systèmes d'´ equations aux dérivées partiellesàpartiellesà deux variables indépendantes. Arkiv for matematik , astronomi och fysik, pp.1-9, 1938.

J. Cheng, M. Choulli, and J. Lin, STABLE DETERMINATION OF A BOUNDARY COEFFICIENT IN AN ELLIPTIC EQUATION, Mathematical Models and Methods in Applied Sciences, vol.18, issue.01, pp.107-123, 2008.
DOI : 10.1142/S0218202508002620

C. Fabre and G. Lebeau, Prolongement unique des solutions de l'´ equation de Stokes, Communication in Partial Differential Equations, pp.573-596, 1996.
DOI : 10.1080/03605309608821198

A. Fursikov and O. Imanuvilov, Controllability of Evolution Equations, Lecture Notes series 34, 1996.

P. Grisvard, Elliptic problems in nonsmooth domains, 1985.
DOI : 10.1137/1.9781611972030

L. Hormander, Linear Partial Differential Operators, Fourth Printing, 1976.

V. Isakov, Inverse problems for partial differential equations, 1998.

F. John, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Communications on Pure and Applied Mathematics, vol.4, issue.4, pp.551-585, 1960.
DOI : 10.1002/cpa.3160130402

M. V. Klibanov and A. A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications, VSP, 2004.
DOI : 10.1515/9783110915549

R. Lattès and J. Lions, Méthode de quasi-réversibilité et applications. Dunod, 1967.

M. M. Lavrentiev, V. G. Romanov, and S. P. Shishatskii, Ill-posed problems in mathematical physics and analysis, Amer. Math. Soc, 1986.

G. Lebeau and L. Robbiano, Contr??le Exact De L??quation De La Chaleur, Communications in Partial Differential Equations, vol.52, issue.1-2, pp.335-356, 1995.
DOI : 10.1016/0022-0396(87)90043-X

L. E. Payne, On a Priori Bounds in the Cauchy Problem for Elliptic Equations, SIAM Journal on Mathematical Analysis, vol.1, issue.1, pp.82-89, 1970.
DOI : 10.1137/0501008

K. Phung, Remarques sur l'observabilité pour l'´ equation de Laplace. ESAIM : Control, Optimisation and Calculus of Variations, pp.621-635, 2003.
DOI : 10.1051/cocv:2003030

URL : http://archive.numdam.org/article/COCV_2003__9__621_0.pdf

L. Robbiano, Théorème d'unicité adapté au contrôle des solutions des probì emes hyperboliques. Communication in Partial Differential Equations, pp.789-800, 1991.
DOI : 10.5802/jedp.409

URL : http://archive.numdam.org/article/JEDP_1991____A7_0.pdf

E. Sincich, Stability and reconstruction for the determination of boundary terms by a single measurement, Thesis. SISSA/ISAS, 2005.
URL : https://hal.archives-ouvertes.fr/tel-00171273

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