Un théorème de régularité pour les minimiseurs de Mumford-Shah dans ℝ 3

Antoine Lemenant[1]

  • [1] Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Boîte courrier 187 75252 Paris Cedex 05 France

Séminaire Équations aux dérivées partielles (2010-2011)

  • page 1-11

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Lemenant, Antoine. "Un théorème de régularité pour les minimiseurs de Mumford-Shah dans $\mathbb{R}^3$." Séminaire Équations aux dérivées partielles (2010-2011): 1-11. <http://eudml.org/doc/116449>.

@article{Lemenant2010-2011,
affiliation = {Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Boîte courrier 187 75252 Paris Cedex 05 France},
author = {Lemenant, Antoine},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Un théorème de régularité pour les minimiseurs de Mumford-Shah dans $\mathbb\{R\}^3$},
url = {http://eudml.org/doc/116449},
year = {2010-2011},
}

TY - JOUR
AU - Lemenant, Antoine
TI - Un théorème de régularité pour les minimiseurs de Mumford-Shah dans $\mathbb{R}^3$
JO - Séminaire Équations aux dérivées partielles
PY - 2010-2011
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 11
LA - fre
UR - http://eudml.org/doc/116449
ER -

References

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  2. Luigi Ambrosio, Nicola Fusco, and Diego Pallara. Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, 2000.  Zbl0957.49001MR1857292
  3. Luigi Ambrosio and Diego Pallara. Partial regularity of free discontinuity sets. I. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(1) :1–38, 1997.  Zbl0896.49023MR1475771
  4. A. Bonnet. On the regularity of edges in image segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 13(4) :485–528, 1996.  Zbl0883.49004MR1404319
  5. Guy David. C 1 + α -regularity for two dimensional almost-minimal sets in ℝ n . (2008) Preprint Available at http://www.math.u-psud.fr/~gdavid/.  MR2359022
  6. Guy David. C 1 -arcs for minimizers of the Mumford-Shah functional. SIAM J. Appl. Math., 56(3) :783–888, 1996.  Zbl0870.49020MR1389754
  7. Guy David. Singular sets of minimizers for the Mumford-Shah functional, volume 233 of Progress in Mathematics. Birkhäuser Verlag, Basel, 2005.  Zbl1086.49030MR2129693
  8. Guy David. Hölder regularity of two-dimensional almost-minimal sets in ℝ n . Ann. Fac. Sci. Toulouse Math. (6), 18(1) :65–246, 2009.  Zbl1213.49051MR2518104
  9. Guy David, Thierry De Pauw, and Tatiana Toro. A generalization of Reifenberg’s theorem in ℝ 3 . Geom. Funct. Anal., 18(4) :1168–1235, 2008.  Zbl1169.49040MR2465688
  10. E. De Giorgi, M. Carriero, and A. Leaci. Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal., 108(3) :195–218, 1989.  Zbl0682.49002MR1012174
  11. Herbert Koch, Giovanni Leoni, and Massimiliano Morini. On optimal regularity of free boundary problems and a conjecture of De Giorgi. Comm. Pure Appl. Math., 58(8) :1051–1076, 2005.  Zbl1082.35168MR2143526
  12. Antoine Lemenant. Regularity of the singular set for Mumford-Shah minimizers in ℝ 3 near a minimal cone. To apear in Ann. Scu. Norm. Sup. Pisa.  Zbl1239.49062
  13. Antoine Lemenant. Sur la régularité des minimiseurs de Mumford-Shah en dimension 3 et supérieure. Thesis Université Paris Sud XI, Orsay, 2008.  
  14. Antoine Lemenant. Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets. Ann. Scuola Norm. Sup. Pisa Cl. Sci., IX(5) :1–34, 2010.  Zbl1197.49050
  15. David Mumford and Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42(5) :577–685, 1989.  Zbl0691.49036MR997568
  16. Jean E. Taylor. The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Ann. of Math. (2), 103(3) :489–539, 1976.  Zbl0335.49032MR428181

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