On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone

Antoine Lemenant

Rendiconti del Seminario Matematico della Università di Padova (2009)

  • Volume: 122, page 129-159
  • ISSN: 0041-8994

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Lemenant, Antoine. "On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 129-159. <http://eudml.org/doc/108766>.

@article{Lemenant2009,
author = {Lemenant, Antoine},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {homogeneity of global minimizers; Mumford-Shah functional},
language = {eng},
pages = {129-159},
publisher = {Seminario Matematico of the University of Padua},
title = {On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone},
url = {http://eudml.org/doc/108766},
volume = {122},
year = {2009},
}

TY - JOUR
AU - Lemenant, Antoine
TI - On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 129
EP - 159
LA - eng
KW - homogeneity of global minimizers; Mumford-Shah functional
UR - http://eudml.org/doc/108766
ER -

References

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  1. [1] R. A. ADAMS, Sobolev spaces. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], Pure and Applied Mathematics, Vol. 65 (New YorkLondon, 1975). Zbl0314.46030MR450957
  2. [2] L. AMBROSIO - N. FUSCO - D. PALLARA, Partial regularity of free discontinuity sets. II. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24 (1) ( 1997), pp. 39-62. Zbl0896.49024MR1475772
  3. [3] L. AMBROSIO - N. FUSCO - D. PALLARA, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press (New York, 2000). Zbl0957.49001MR1857292
  4. [4] A. BONNET, On the regularity of edges in image segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (4) (1996), pp. 485-528. Zbl0883.49004MR1404319
  5. [5] M. DAUGE, Elliptic boundary value problems on corner domains, volume 1341 of Lecture Notes in Mathematics. Smoothness and asymptotics of solutions (Springer-Verlag, Berlin, 1988). Zbl0668.35001MR961439
  6. [6] M. DAUGE, Neumann and mixed problems on curvilinear polyhedra. Integral Equations Operator Theory, 15 (2) (1992), pp. 227-261. Zbl0767.46026MR1147281
  7. [7] G. DAVID, C1 -arcs for minimizers of the Mumford-Shah functional. SIAM J. Appl. Math., 56 (3) (1996), pp. 783-888. Zbl0870.49020MR1389754
  8. [8] G. DAVID, Singular sets of minimizers for the Mumford-Shah functional, volume 233 of Progress in Mathematics (Birkhäuser Verlag, Basel, 2005). Zbl1086.49030MR2129693
  9. [9] G. DAVID, Hölder regularity of two dimensional almost-minimal sets in Rn . Geom. Funct. Anal., 18 (4) (2008), pp. 1168-1235. Zbl1169.49040
  10. [10] G. DAVID - D. P. THIERRY - T. TORO, A generalisation of Reifenberg's theorem in R3 . Ann. Fac. Sc. Toul. (6), 18 (1) (2009), pp. 65-246. 
  11. [11] E. DE GIORGI - M. CARRIERO - A. LEACI, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal., 108 (3) (1989), pp. 195-218. Zbl0682.49002MR1012174
  12. [12] D. GILBARG - N. S. TRUDINGER, Elliptic partial differential equations of second order, volume 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. (Springer-Verlag, Berlin, second edition, 1983). Zbl0562.35001MR737190
  13. [13] J. B. KELLER, Singularities at the tip of a plane angular sector. J. Math. Phys., 40 (2) (1999), pp. 1087-1092. Zbl0947.35039MR1674215
  14. [14] V. A. KOZLOV - V. G. MAZH YA - J. ROSSMANN, Spectral problems associated with corner singularities of solutions to elliptic equations, volume 85 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2001. Zbl0965.35003MR1788991
  15. [15] A. LEMENANT, Sur la régularité des minimiseurs de Mumford-Shah en dimension 3 et supérieure. Thesis Université Paris Sud XI (Orsay, 2008). 
  16. [16] P. LÉVY-BRUHL, Introduction à la théorie spectrale. Dunod, 2003. 
  17. [17] BENOÎT MERLET, Numerical study of a new global minimizer for the Mumford-Shah functional in R3 . ESAIM Control Optim. Calc. Var., 13 (3) (2007), pp. 553-569. Zbl1152.49045MR2329176
  18. [18] D. MUMFORD - J. SHAH, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42, (5) (1989), pp. 577-685. Zbl0691.49036MR997568
  19. [19] M. REED - B. SIMON, Methods of modern mathematical physics. IV. Analysis of operators. Academic Press [Harcourt Brace Jovanovich Publishers], (New York, 1978). Zbl0401.47001MR493421
  20. [20] J. E. TAYLOR, The structure of singularities in soap-bubble-like and soapfilm-like minimal surfaces. Ann. of Math. (2), 103 (3) (1976), pp. 489-539. Zbl0335.49032MR428181
  21. [21] M. E. TAYLOR, Partial Differential Equations Basic Theory, Vol. 23 of Texts in Applied Mathematics. (Springer, 1st ed. 1996). (Corr. 2nd printing, 1999). Zbl0869.35001MR1395147

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