Some remarks on uniqueness and regularity of Cheeger sets
Caselles, V. ; Novaga, M. ; Chambolle, A.
Rendiconti del Seminario Matematico della Università di Padova, Tome 124 (2010), p. 191-202 / Harvested from Numdam
Publié le : 2010-01-01
@article{RSMUP_2010__123__191_0,
     author = {Caselles, V. and Novaga, M. and Chambolle, A.},
     title = {Some remarks on uniqueness and regularity of Cheeger sets},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {124},
     year = {2010},
     pages = {191-202},
     mrnumber = {2683297},
     zbl = {1198.49042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2010__123__191_0}
}
Caselles, V.; Novaga, M.; Chambolle, A. Some remarks on uniqueness and regularity of Cheeger sets. Rendiconti del Seminario Matematico della Università di Padova, Tome 124 (2010) pp. 191-202. http://gdmltest.u-ga.fr/item/RSMUP_2010__123__191_0/

[1] F. Alter - V. Caselles, Uniqueness of the Cheeger set of a convex body. To appear in Nonlinear Analysis, TMA. | MR 2468216 | Zbl 1167.52005

[2] F. Alter - V. Caselles - A. Chambolle, Evolution of Convex Sets in the Plane by the Minimizing Total Variation Flow, Interfaces and Free Boundaries, 7 (2005), pp. 29--53. | MR 2126142 | Zbl 1084.49003

[3] F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in N , Math. Ann., 332 (2005), pp. 329--366. | MR 2178065 | Zbl 1108.35073

[4] L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime, Scuola Normale Superiore, Pisa, 1997. | MR 1736268 | Zbl 0977.49028

[5] L. Ambrosio - N. Fusco - D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, 2000. | MR 1857292 | Zbl 0957.49001

[6] G. Bellettini - V. Caselles - M. Novaga, The Total Variation Flow in N , J. Differential Equations, 184 (2002), pp. 475--525. | MR 1929886 | Zbl 1036.35099

[7] G. Buttazzo - G. Carlier - M. Comte, On the selection of maximal Cheeger sets, Differential and Integral Equations, 20 (9) (2007), pp. 991--1004. | MR 2349376 | Zbl pre05808156

[8] E. Barozzi - U. Massari, Regularity of minimal boundaries with obstacles, Rend. Sem. Mat. Univ. Padova, 66 (1982), pp. 129--135. | Numdam | MR 664576 | Zbl 0494.49030

[9] L. A. Caffarelli, The obstacle problem revisited, The Journal of Fourier Analysis and Applications, 4 (1998), pp. 383--402. | MR 1658612 | Zbl 0928.49030

[10] L. A. Caffarelli - N. M. Riviere, On the rectifiability of domains with finite perimeter, Ann. Scuola Normale Superiore di Pisa, 3 (1976), pp. 177--186. | Numdam | MR 410539 | Zbl 0362.49031

[11] G. Carlier - M. Comte, On a weighted total variation minimization problem, J. Funct. Anal., 250 (2007), pp. 214--226. | MR 2345913 | Zbl 1120.49011

[12] G. Carlier - M. Comte - G. Peyré, Approximation of maximal Cheeger sets by projection, Preprint (2007). | Numdam | MR 2494797

[13] V. Caselles - A. Chambolle - M. Novaga, Uniqueness of the Cheeger set of a convex body, Pacific Journal of Mathematics, 232 (1) (2007), pp. 77--90. | MR 2358032 | Zbl pre05366256

[14] A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20 (2004), pp. 89--97. | MR 2049783

[15] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, Princeton Univ. Press, Princeton (New Jersey, 1970), pp. 195--199. | MR 402831 | Zbl 0212.44903

[16] D. Gilbarg - N. S. Trudinger, Elliptic partial Differential Equations of Second Order, Springer Verlag, 1998.

[17] E. Giusti, On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions, Invent. Math., 46 (1978), pp. 111--137. | MR 487722 | Zbl 0381.35035

[18] E. H. A. Gonzalez - U. Massari - I. Tamanini, Minimal boundaries enclosing a given volume, Manuscripta Math., 34 (1981), pp. 381--395. | MR 620458 | Zbl 0481.49035

[19] E. Gonzalez - U. Massari - I. Tamanini, On the regularity of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. Journal, 32 (1983), pp. 25--37. | MR 684753 | Zbl 0486.49024

[20] D. Grieser, The first eigenvalue of the Laplacian, isoperimetric constants, and the max-flow min-cut theorem, Arch. Math., 87 (1) (2006), pp. 75--85. | MR 2246409 | Zbl 1105.35062

[21] L. Lefton - D. Wei, Numerical approximation of the first eigenpair of the p-laplacian using finite elements and the penalty method, Numer. Funct. Anal. Optim., 18 (3-4) (1997), pp. 389--399. | MR 1448898 | Zbl 0884.65103

[22] B. Kawohl - V. Fridman, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolinae, 44 (2003), pp. 659--667. | MR 2062882 | Zbl 1105.35029

[23] B. Kawohl, T. Lachand-Robert, Characterization of Cheeger sets for convex subsets of the plane, Pacific J. Math., 225 (1) (2006), pp. 103--118. | MR 2233727 | Zbl 1133.52002

[24] B. Kawohl - M. Novaga, The p-Laplace eigenvalue problem as p1 and Cheeger sets in a Finsler metric, J. Convex Anal., 15 (3) (2008), pp. 623--634. | MR 2431415 | Zbl 1186.35115

[25] U. Massari, Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in n , Arch. Rat. Mech. Anal., 55 (1974), pp. 357--382. | MR 355766 | Zbl 0305.49047

[26] P. Marcellini - K. Miller, Asymptotic growth for the parabolic equation of prescribed mean curvature, J. Differential Equations, 51 (3) (1984), pp. 326--358. | MR 735204 | Zbl 0545.35044

[27] G. Strang, Maximal flow through a domain, Math. Programming, 26 (2) (1983), pp. 123--143. | MR 700642 | Zbl 0513.90026

[28] E. Stredulinsky - W. P. Ziemer, Area minimizing sets subject to a volume constraint in a convex set, J. Geom. Anal., 7 (1997), pp. 653--677. | MR 1669207 | Zbl 0940.49025

[29] J. Taylor, Boundary regularity for solutions to various capillarity and free boundary problems, Comm. in Partial Differential Equations, 2 (1977), 323--357. | MR 487721 | Zbl 0357.35010