On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
Lemenant, Antoine
Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), p. 129-159 / Harvested from Numdam
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Publié le : 2009-01-01
@article{RSMUP_2009__122__129_0,
     author = {Lemenant, Antoine},
     title = {On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {122},
     year = {2009},
     pages = {129-159},
     mrnumber = {2582834},
     zbl = {1187.49035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2009__122__129_0}
}

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, Tome 122 (2009) pp. 129-159. http://gdmltest.u-ga.fr/item/RSMUP_2009__122__129_0/

[1] R. A. Adams, Sobolev spaces. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], Pure and Applied Mathematics, Vol. 65 (New YorkLondon, 1975). | MR 450957 | Zbl 0314.46030

[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. | Numdam | MR 1475772 | Zbl 0896.49024

[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). | MR 1857292 | Zbl 0957.49001

[4] A. Bonnet, On the regularity of edges in image segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (4) (1996), pp. 485-528. | Numdam | MR 1404319 | Zbl 0883.49004

[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). | MR 961439 | Zbl 0668.35001

[6] M. Dauge, Neumann and mixed problems on curvilinear polyhedra. Integral Equations Operator Theory, 15 (2) (1992), pp. 227-261. | MR 1147281 | Zbl 0767.46026

[7] G. David, C1 -arcs for minimizers of the Mumford-Shah functional. SIAM J. Appl. Math., 56 (3) (1996), pp. 783-888. | MR 1389754 | Zbl 0870.49020

[8] G. David, Singular sets of minimizers for the Mumford-Shah functional, volume 233 of Progress in Mathematics (Birkhäuser Verlag, Basel, 2005). | MR 2129693 | Zbl 1086.49030

[9] G. David, Hölder regularity of two dimensional almost-minimal sets in Rn . Geom. Funct. Anal., 18 (4) (2008), pp. 1168-1235.

[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] 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. | MR 1012174 | Zbl 0682.49002

[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). | MR 737190 | Zbl 0562.35001

[13] J. B. Keller, Singularities at the tip of a plane angular sector. J. Math. Phys., 40 (2) (1999), pp. 1087-1092. | MR 1674215 | Zbl 0947.35039

[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. | MR 1788991 | Zbl 0965.35003

[15] A. Lemenant, Sur la régularité des minimiseurs de Mumford-Shah en dimension 3 et supérieure. Thesis Université Paris Sud XI (Orsay, 2008).

[16] P. Lévy-Bruhl, Introduction à la théorie spectrale. Dunod, 2003.

[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. | Numdam | MR 2329176 | Zbl 1152.49045

[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. | MR 997568 | Zbl 0691.49036

[19] M. Reed - B. Simon, Methods of modern mathematical physics. IV. Analysis of operators. Academic Press [Harcourt Brace Jovanovich Publishers], (New York, 1978). | MR 493421 | Zbl 0401.47001

[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. | MR 428181 | Zbl 0335.49032

[21] M. E. Taylor, Partial Differential Equations Basic Theory, Vol. 23 of Texts in Applied Mathematics. (Springer, 1st ed. 1996). (Corr. 2nd printing, 1999). | MR 1395147 | Zbl 0869.35001