Free access
Issue
ESAIM: COCV
Volume 13, Number 3, July-September 2007
Page(s) 553 - 569
DOI http://dx.doi.org/10.1051/cocv:2007026
Published online 20 June 2007
  1. M. Amara and M.-A. Moussaoui, Approximation of solutions and singularities coefficients for an elliptic problem in a plane polygonal domain. Note Technique, E.N.S. Lyon (1989).
  2. A. Bonnet, On the regularity of edges in image segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 485–528.
  3. M. Bourlard, M. Dauge, M.S Lubuma and S. Nicaise, Coefficients of the singularities for elliptic boundary value problems on domains with conical points. III. Finite element methods on polygonal domains. SIAM J. Numer. Anal. 29 (1992) 136–155. [CrossRef] [MathSciNet]
  4. P. Ciarlet, Jr. and J. He, The singular complement method for 2d scalar problems. C. R. Math. Acad. Sci. Paris 336 (2003) 353–358. [CrossRef] [MathSciNet]
  5. M. Dauge, Elliptic boundary value problems on corner domains, Lect. Notes Math. 1341. Smoothness and asymptotics of solutions. Springer-Verlag, Berlin (1988).
  6. M. Dauge, S. Nicaise, M. Bourlard and M.S. Lubuma, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I. Résultats généraux pour le problème de Dirichlet. RAIRO Modél. Math. Anal. Numér. 24 (1990) 27–52. [MathSciNet]
  7. M. Dauge, S. Nicaise, M. Bourlard and M.S. Lubuma, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II. Quelques opérateurs particuliers. RAIRO Modél. Math. Anal. Numér. 24 (1990) 343–367. [MathSciNet]
  8. G. David, Singular sets of minimizers for the Mumford-Shah functional. Progress Math. 233, Birkhäuser Verlag, Basel (2005).
  9. E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational. Mech. Anal. 108 (1989) 195–218. [CrossRef] [MathSciNet]
  10. A. Ern and J.-L Guermond, Éléments finis: théorie, applications, mise en œ uvre. Math. Appl. 36, Springer-Verlag, Berlin (2002).
  11. P. Grisvard, Singularities in boundary value problems, Recherches Math. Appl. 22. Masson, Paris (1992).
  12. V.A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obšč. 16 (1967) 209–292. [MathSciNet]
  13. M.-A. Moussaoui, Sur l'approximation des solutions du problème de Dirichlet dans un ouvert avec coins, in Singularities and constructive methods for their treatment (Oberwolfach, 1983). Lect. Notes Math. 1121, Springer, Berlin (1985) 199–206.
  14. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989) 577–685. [CrossRef] [MathSciNet]