Free Access
Issue
ESAIM: M2AN
Volume 44, Number 4, July-August 2010
Page(s) 715 - 735
DOI https://doi.org/10.1051/m2an/2010016
Published online 23 February 2010
  1. G. Alessandrini, E. Beretta, E. Rosset and S. Vessella, Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Ann. Scuola Norm. Sup. Pisa 29 (2000) 755–806. [Google Scholar]
  2. L. Bourgeois, Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation. Inv. Prob. 22 (2006) 413–430. [CrossRef] [Google Scholar]
  3. L. Bourgeois and J. Dardé, Conditional stability for ill-posed elliptic Cauchy problems: the case of Lipschitz domains (part II). Rapport INRIA 6588, France (2008). [Google Scholar]
  4. A.L. Bukhgeim, Extension of solutions of elliptic equations from discrete sets. J. Inv. Ill-Posed Problems 1 (1993) 17–32. [CrossRef] [Google Scholar]
  5. T. Carleman, Sur un problème d'unicité pour les systèmes d'équations aux dérivées partielles à deux variables indépendantes. Ark. Mat. Astr. Fys. 26 (1939) 1–9. [Google Scholar]
  6. J. Cheng, M Choulli and J. Lin, Stable determination of a boundary coefficient in an elliptic equation. M3AS 18 (2008) 107–123. [Google Scholar]
  7. M.C. Delfour and J.-P. Zolésio, Shapes and geometries. SIAM, USA (2001). [Google Scholar]
  8. C. Fabre and G. Lebeau, Prolongement unique des solutions de l'équation de Stokes. Comm. Part. Differ. Equ. 21 (1996) 573–596. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Fursikov and O. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series 34. Research Institute of Mathematics, Seoul National University, South Korea (1996). [Google Scholar]
  10. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, USA (1985). [Google Scholar]
  11. L. Hormander, Linear Partial Differential Operators. Fourth Printing, Springer-Verlag, Germany (1976). [Google Scholar]
  12. T. Hrycak and V. Isakov, Increased stability in the continuation of solutions to the Helmholtz equation. Inv. Prob. 20 (2004) 697–712. [CrossRef] [Google Scholar]
  13. V. Isakov, Inverse problems for partial differential equations. Springer-Verlag, Berlin, Germany (1998). [Google Scholar]
  14. F. John, Continuous dependence on data for solutions of pde with a prescribed bound. Commun. Pure Appl. Math. 13 (1960) 551–585. [Google Scholar]
  15. M.V. Klibanov, Estimates of initial conditions of parabolic equations and inequalities via lateral data. Inv. Prob. 22 (2006) 495–514. [CrossRef] [Google Scholar]
  16. M.V. Klibanov and A.A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. VSP (2004). [Google Scholar]
  17. R. Lattès and J.-L. Lions, Méthode de quasi-réversibilité et applications. Dunod, France (1967). [Google Scholar]
  18. M.M. Lavrentiev, V.G. Romanov and S.P. Shishatskii, Ill-posed problems in mathematical physics and analysis. Amer. Math. Soc., Providence, USA (1986). [Google Scholar]
  19. G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur. Commun. Partial Differ. Equ. 20 (1995) 335–356. [Google Scholar]
  20. L.E. Payne, On a priori bounds in the Cauchy problem for elliptic equations. SIAM J. Math. Anal. 1 (1970) 82–89. [CrossRef] [MathSciNet] [Google Scholar]
  21. K.-D. Phung, Remarques sur l'observabilité pour l'équation de Laplace. ESAIM: COCV 9 (2003) 621–635. [EDP Sciences] [Google Scholar]
  22. L. Robbiano, Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques. Commun. Partial Differ. Equ. 16 (1991) 789–800. [Google Scholar]
  23. D.A. Subbarayappa and V. Isakov, On increased stability in the continuation of the Helmholtz equation. Inv. Prob. 23 (2007) 1689–1697. [CrossRef] [Google Scholar]
  24. T. Takeuchi and M. Yamamoto, Tikhonov regularization by a reproducing kernel Hilbert space for the Cauchy problem for a elliptic equation. SIAM J. Sci. Comput. 31 (2008) 112–142. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you