Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 41
Number of page(s) 43
DOI https://doi.org/10.1051/cocv/2026023
Published online 06 May 2026
  1. A.P. Calderón, On an inverse boundary value problem. Comput. Appl. Math. 25 (2006) 133–138. [Google Scholar]
  2. G. Uhlmann, 30 years of Calderón's problem, Seminaire Laurent Schwartz-Équations aux dérivées partielles et applications. Année (2012-2013) 25. [Google Scholar]
  3. M. Cheney, D. Isaacson and J.C. Newell, Electrical impedance tomography. SIAM Rev. 41 (1999) 85–101. [Google Scholar]
  4. J. Jordana, M. Gasulla and R. Pallás-Areny, Electrical resistance tomography to detect leaks from buried pipes. Meas. Sci. Technol. 12 (2001) 1061–1068. [Google Scholar]
  5. J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153–169. [Google Scholar]
  6. A.L. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data. Commun. Part. Diff. Equ. 27 (2002) 653–668. [Google Scholar]
  7. V. Isakov, On uniqueness in the inverse conductivity problem with local data. Inverse Probl. Imaging 1 (2007) 95–105. [Google Scholar]
  8. C. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data. Ann. Math. 165 (2007) 567–591. [Google Scholar]
  9. K. Krupchyk and G. Uhlmann, Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit. J. Math. Pures Appl. 126 (2019) 273–291. [Google Scholar]
  10. R.-Y. Lai, X. Lu and T. Zhou, Partial data inverse problems for the nonlinear time-dependent Schrödinger equation. SIAM J. Math. Anai. 56 (2024) 4712–4741. [Google Scholar]
  11. R.-Y. Lai and T. Zhou, An inverse problem for the non-linear fractional magnetic Schrodinger equation. J. Diff. Equ. 343 (2023) 64–89. [Google Scholar]
  12. R.-Y. Lai and T. Zhou, Partial data inverse problems for nonlinear magnetic Schröodinger equations. Math. Res. Lett. 30 (2023) 1535–1563. [Google Scholar]
  13. X. Zhao and G. Yuan, Stability estimates for an inverse problem for Schroödinger operators at high frequencies from arbitrary partial boundary measurements. Inverse Probl. 39 (2023) 125009, 21. [Google Scholar]
  14. C. Kenig and M. Salo, Recent progress in the Calderón problem with partial data, in Inverse Problems and Applications. Contemporary Mathematics, vol. 615. American Mathematical Society, Providence, RI (2014) 193–222. [Google Scholar]
  15. M. Horváth and Z. Markó, Discrete inverse problems for the Schrodinger operator on the multi-dimensional square lattice with partial Cauchy data. Inverse Probl. 32 (2016) 055006, 9. [Google Scholar]
  16. S. Ervedoza and F. De Gournay, Uniform stability estimates for the discrete Calderón problems. Inverse Probl. 27 (2011) 125012, 37. [Google Scholar]
  17. R. Lecaros, J.H. Ortega, A. Pérez and L. De Teresa, Discrete Calderón problem with partial data. Inverse Probl. 39 (2023) 035001, 28. [Google Scholar]
  18. L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques. Asymptot. Anal. 10 (1995) 95–115. [Google Scholar]
  19. F. Boyer, V. Hernádez-Santamaría and L.D. Teresa, Insensitizing controls for a semilinear parabolic equation: a numerical approach. Math. Control Reiat. Fieids 9 (2019) 117–158. [Google Scholar]
  20. F. Boyer, F. Hubert and J.L. Rousseau, Discrete Carleman estimates for elliptic operators in arbitrary dimension and applications. SIAM J. Control Optim,. 48 (2010) 5357–5397. [Google Scholar]
  21. F. Boyer, F. Hubert and J.L. Rousseau, Uniform controllability properties for space/time-discretized parabolic equations. Numer. Math. 118 (2011) 601–661. [Google Scholar]
  22. F. Boyer and J.L. Rousseau, Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations. Ann. Inst. H. Poincaré C Anal. Non Linéaire 31 (2014) 1035–1078. [Google Scholar]
  23. E. Cerpa, R. Lecaros, T.N.T. Nguyen and A. Pérez, Carleman estimates and controllability for a semi-discrete fourth-order parabolic equation. J. Math. Pures Appl. 164 (2022) 93–130. [Google Scholar]
  24. T.N.T. Nguyen, Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability. Math. Control Relat. Fields 4 (2014) 203–259. [Google Scholar]
  25. F. Boyer and V. Hernandez-Santamaría, Carleman estimates for time-discrete parabolic equations and applications to controllability. ESAIM Control Optim. Calc. Var. 26 (2020) 43. [Google Scholar]
  26. P.G. Casanova and V. Hernández-Santamaría, Carleman estimates and controllability results for fully discrete approximations of 1D parabolic equations. Adv. Comput. Math. 47 (2021) 71. [Google Scholar]
  27. R. Lecaros, R. Morales, A. Pérez and S. Zamorano, Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions. J. Diff. Equ. 365 (2023) 832–881. [Google Scholar]
  28. L. Baudouin and S. Ervedoza, Convergence of an inverse problem for a 1-D discrete wave equation. SIAM J. Control Optim. 51 (2013) 556–598. [Google Scholar]
  29. L. Baudouin, S. Ervedoza and A. Osses, Stability of an inverse problem for the discrete wave equation and convergence results. J. Math. Pures Appl. 103 (2015) 1475–1522. [Google Scholar]
  30. W. Zhang and Z. Zhao, Convergence analysis of a coefficient inverse problem for the semi-discrete damped wave equation. Appl. Anal. 101 (2022) 1430–1455. [Google Scholar]
  31. Z. Zhao and W. Zhang, Stability of a coefficient inverse problem for the discrete Schrödinger equation and a convergence result. J. Math. Anal. Appl. 518 (2023) 126665, 25. [Google Scholar]
  32. B. Wu, Y. Wang and Z. Wang, Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation and its applications. Inverse Probl. 40 (2024) 115003, 33. [Google Scholar]
  33. A. Fernández-Bertolin, L. Roncal, A. Rüland and D. Stan, Discrete Carleman estimates and three balls inequalities. Calc. Var. Part. Diff. Equ. 60 (2021) 28. [Google Scholar]
  34. G. Alessandrini, Stable determination of conductivity by boundary measurements. Appl. Anal. 27 (1988) 153–172. [Google Scholar]
  35. A. Ruland and M. Salo, Quantitative Runge approximation and inverse problems. Int. Math. Res. Not. 20 (2019) 6216–6234. [Google Scholar]
  36. F. Boyer, F. Hubert and J.L. Rousseau, Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations. J. Math. Pures Appl. 93 (2010) 240–276. [Google Scholar]
  37. R. Lecaros, J.H. Ortega and A. Pérez, Stability estimate for the semi-discrete linearized Benjamin-Bona-Mahony equation. ESAIM Control Optim. Calc. Var. 27 (2021) 30. [Google Scholar]
  38. A.V. Fursikov and O.Y. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, vol. 34. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  39. J.L. Rousseau and G. Lebeau, On Carleman estimates for elliptic and parabolic operators. ESAIM Control Optim. Calc. Var. 18 (2012) 712–747. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  40. M. Bellassoued, Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation. Inverse Probl. 20 (2004) 1033–1052. [Google Scholar]
  41. M. Bellassoued and M. Yamamoto, Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation. J. Math. Pures Appl. 85 (2006) 193–224. [Google Scholar]
  42. G. Lebeau and L. Robbiano, Controle exact de l'équation de la chaleur. Commun. Part. Diff. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]

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