Some remarks on uniqueness and regularity of Cheeger sets
V. Caselles; M. Novaga; A. Chambolle
Rendiconti del Seminario Matematico della Università di Padova (2010)
- Volume: 123, page 191-202
- ISSN: 0041-8994
Access Full Article
topHow to cite
topCaselles, V., Novaga, M., and Chambolle, A.. "Some remarks on uniqueness and regularity of Cheeger sets." Rendiconti del Seminario Matematico della Università di Padova 123 (2010): 191-202. <http://eudml.org/doc/242646>.
@article{Caselles2010,
author = {Caselles, V., Novaga, M., Chambolle, A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {maximal and minimal Cheeger sets; regularity of Cheeger sets; Cheeger set},
language = {eng},
pages = {191-202},
publisher = {Seminario Matematico of the University of Padua},
title = {Some remarks on uniqueness and regularity of Cheeger sets},
url = {http://eudml.org/doc/242646},
volume = {123},
year = {2010},
}
TY - JOUR
AU - Caselles, V.
AU - Novaga, M.
AU - Chambolle, A.
TI - Some remarks on uniqueness and regularity of Cheeger sets
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2010
PB - Seminario Matematico of the University of Padua
VL - 123
SP - 191
EP - 202
LA - eng
KW - maximal and minimal Cheeger sets; regularity of Cheeger sets; Cheeger set
UR - http://eudml.org/doc/242646
ER -
References
top- [1] F. Alter - V. Caselles, Uniqueness of the Cheeger set of a convex body. To appear in Nonlinear Analysis, TMA. Zbl1167.52005MR2468216
- [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. Zbl1084.49003MR2126142
- [3] F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in , Math. Ann., 332 (2005), pp. 329--366. Zbl1108.35073MR2178065
- [4] L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime, Scuola Normale Superiore, Pisa, 1997. Zbl0977.49028MR1736268
- [5] L. Ambrosio - N. Fusco - D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, 2000. Zbl0957.49001MR1857292
- [6] G. Bellettini - V. Caselles - M. Novaga, The Total Variation Flow in , J. Differential Equations, 184 (2002), pp. 475--525. Zbl1036.35099MR1929886
- [7] G. Buttazzo - G. Carlier - M. Comte, On the selection of maximal Cheeger sets, Differential and Integral Equations, 20 (9) (2007), pp. 991--1004. Zbl1212.49019MR2349376
- [8] E. Barozzi - U. Massari, Regularity of minimal boundaries with obstacles, Rend. Sem. Mat. Univ. Padova, 66 (1982), pp. 129--135. Zbl0494.49030MR664576
- [9] L. A. Caffarelli, The obstacle problem revisited, The Journal of Fourier Analysis and Applications, 4 (1998), pp. 383--402. Zbl0928.49030MR1658612
- [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. Zbl0362.49031MR410539
- [11] G. Carlier - M. Comte, On a weighted total variation minimization problem, J. Funct. Anal., 250 (2007), pp. 214--226. Zbl1120.49011MR2345913
- [12] G. Carlier - M. Comte - G. Peyré, Approximation of maximal Cheeger sets by projection, Preprint (2007). Zbl1161.65046MR2494797
- [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. Zbl1221.35171MR2358032
- [14] A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20 (2004), pp. 89--97. MR2049783
- [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. Zbl0212.44903MR402831
- [16] D. Gilbarg - N. S. Trudinger, Elliptic partial Differential Equations of Second Order, Springer Verlag, 1998. Zbl1042.35002
- [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. Zbl0381.35035MR487722
- [18] E. H. A. Gonzalez - U. Massari - I. Tamanini, Minimal boundaries enclosing a given volume, Manuscripta Math., 34 (1981), pp. 381--395. Zbl0481.49035MR620458
- [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. Zbl0486.49024MR684753
- [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. Zbl1105.35062MR2246409
- [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. Zbl0884.65103MR1448898
- [22] B. Kawohl - V. Fridman, Isoperimetric estimates for the first eigenvalue of the -Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolinae, 44 (2003), pp. 659--667. Zbl1105.35029MR2062882
- [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. Zbl1133.52002MR2233727
- [24] B. Kawohl - M. Novaga, The -Laplace eigenvalue problem as and Cheeger sets in a Finsler metric, J. Convex Anal., 15 (3) (2008), pp. 623--634. Zbl1186.35115MR2431415
- [25] U. Massari, Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in , Arch. Rat. Mech. Anal., 55 (1974), pp. 357--382. Zbl0305.49047MR355766
- [26] P. Marcellini - K. Miller, Asymptotic growth for the parabolic equation of prescribed mean curvature, J. Differential Equations, 51 (3) (1984), pp. 326--358. Zbl0545.35044MR735204
- [27] G. Strang, Maximal flow through a domain, Math. Programming, 26 (2) (1983), pp. 123--143. Zbl0513.90026MR700642
- [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. Zbl0940.49025MR1669207
- [29] J. Taylor, Boundary regularity for solutions to various capillarity and free boundary problems, Comm. in Partial Differential Equations, 2 (1977), 323--357. Zbl0357.35010MR487721
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.