EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 7 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 7
Number of page(s) 16
DOI https://doi.org/10.1051/cocv/2025093
Published online 09 February 2026
  1. F. Caubet, J. Dardé and M. Godoy, On the data completion problem and the inverse obstacle problem with partial Cauchy data for Laplace's equation. ESAIM Control Optim. Calc. Var. 25 (2019) Paper No. 30, 30. [Google Scholar]
  2. J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations (1923). [Google Scholar]
  3. F. Ben Belgacem, Why is the Cauchy problem severely ill-posed? Inverse Probl. 23 (2007) 823–836. [Google Scholar]
  4. F. Ben Belgacem and H. El Fekih, On Cauchy's problem. I. A variational Steklov-Poincare theory. Inverse Probl. 21 (2005) 1915–1936. [Google Scholar]
  5. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Vol. 93 of Appl. Math. Sci., 4th expanded edn. Springer, Cham (2019). [Google Scholar]
  6. L. Bourgeois and J. Darde, The "exterior approach" to solve the inverse obstacle problem for the stokes system. Inverse Probl. Imaging 8 (2014) 23–51. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Alessandrini, E. Beretta, E. Rosset and S. Vessella, Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29 (2000) 755–806. [Google Scholar]
  8. L. Bourgeois and J. Darde, A quasi-reversibility approach to solve the inverse obstacle problem. Inverse Probl. Imaging 4 (2010) 351–377. [Google Scholar]
  9. J. Darde, The 'exterior approach': a new framework to solve inverse obstacle problems. Inverse Probl. 28 (2012) 015008, 22. [Google Scholar]
  10. R. Potthast, A survey on sampling and probe methods for inverse problems. Inverse Probl. 22 (2006) r1-r47. [Google Scholar]
  11. W. Rundell, Recovering an obstacle using integral equations. Inverse Probl. Imaging 3 (2009) 319–332. [Google Scholar]
  12. H. Haddar and R. Kress, Conformal mappings and inverse boundary value problems. Inverse Probl. 21 (2005) 935–953. [Google Scholar]
  13. L. Afraites, M. Dambrine, K. Eppler and D. Kateb, Detecting perfectly insulated obstacles by shape optimization techniques of order two. Discrete Contin. Dyn. Syst. Ser. B 8 (2007) 389–416. [Google Scholar]
  14. M. Badra, F. Caubet and M. Dambrine, Detecting an obstacle immersed in a fluid by shape optimization methods. Math. Models Methods Appl. Sci. 21 (2011) 2069–2101. [Google Scholar]
  15. F. Caubet, Instability of an inverse problem for the stationary Navier-Stokes equations. SIAM J. Control Optim. 51 (2013) 2949–2975. [Google Scholar]
  16. A. Henrot and M. Pierre, Variation et optimisation de formes, vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Berlin (2005). Une analyse geometrique. [A geometric analysis]. [Google Scholar]
  17. M. Dambrine, On variations of the shape Hessian and sufficient conditions for the stability of critical shapes. RACSAM. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 96 (2002) 95–121. [Google Scholar]
  18. M. Dambrine and J. Lamboley, Stability in shape optimization with second variation. J. Differ. Equ. 267 (2019) 3009–3045. [Google Scholar]
  19. D. Bucur and G. Buttazzo, Variational methods in shape optimization problems, vol. 65 of Prog. Nonlinear Differ. Equ. Appl. Birkhäuser, Basel (2005). [Google Scholar]
  20. L. Brasco, G. De Philippis and B. Velichkov, Faber-Krahn inequalities in sharp quantitative form. Duke Math. J. 164 (2015) 1777–1831. [Google Scholar]
  21. R. Prunier, Régularité et stabilité en optimisation de forme sous contrainte géométrique. PhD thesis (2023). These de doctorat dirigee par Lamboley, Jimmy et Bucur, Dorin Mathématiques Sorbonne universite 2023. [Google Scholar]
  22. N. Fusco, F. Maggi and A. Pratelli, The sharp quantitative isoperimetric inequality. Ann. Math. 168 (2008) 941–980. [Google Scholar]
  23. M. Dambrine and M. Pierre, About stability of equilibrium shapes. M2AN Math. Model. Numer. Anal. 34 (2000) 811–834. [Google Scholar]
  24. D. Henry, Perturbation of the Boundary in Boundary-value Problems of Partial Differential Equations. vol. 318. Cambridge University Press (2005). [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.