Uniqueness of the Cheeger set of a convex body

Pacific Journal of Mathematics

Volumn 232, Issue 1, 2007, Pages 77-90

  Caselles, Vicent ^a   Chambolle, Antonin ^b   Novaga, Matteo ^c  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

Convex bodies; Variational problems

Indexed keywords

EID: 46449085369     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2007.232.77     Document Type: Article

References (20)

1. F. Alter and V. Caselles, "Uniqueness of the Cheeger set of a convex body", preprint, 2007, Available at benasque.ecm.ub.es/2007pde/talks contr/072cheeger8.pdf.
2. N", Math. Ann. 332:2 (2005), 329-366. MR 2006g:35091 Zbl 02172739.
3. F. Alter, V. Caselles, and A. Chambolle, "Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow", Interfaces Free Bound. 7:1 (2005), 29-53. MR 2006b:35154 Zbl1084.49003.
4. L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford University Press, New York, 2000. MR 2003a:49002 Zbl 0957.49001.
5. F. Andreu, C. Ballester, V. Caselles, and J. Mazón, "The Dirichlet problem for the total variation flow", J. Funct. Anal. 180:2 (2001), 347-403. MR 2001k:35143 Zbl 0973.35109.
6. G. Anzellotti, "Pairings between measures and bounded functions and compensated compactness", Ann. Mat. Pura Appl. (4) 135 (1983), 293-318 (1984). MR 85m:46042 Zbl 0572.46023.
7. G. Anzellotti, "Traces of bounded vector fields and the divergence theorem", preprint, Dipartimento di Matematica, Università di Trento, 1983.
8. N", J. Differential Equations 184:2 (2002), 475-525. MR 2003g:35105 Zbl 1036.35099.
9. H. Brézis and D. Kinderlehrer, "The smoothness of solutions to nonlinear variational inequalities", Indiana Univ. Math. J. 23 (1974), 831-844. MR 50 #13881 Zbl 0278.49011.
10. L. A. Caffarelli and N. M. Rivière, "On the rectifiability of domains with finite perimeter", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3:2 (1976), 177-186. MR 53 #14288 Zbl 0362.49031.
11. N with respect to anisotropic norms", preprint, 2005.
12. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Math. Wissenschaften 224, 1983. Corrected reprint, 1998. MR 2001k:35004 Zbl 0562.35001.
13. E. Giusti, "Boundary value problems for non-parametric surfaces of prescribed mean curvature", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3:3 (1976), 501-548. MR 58 #2572 Zbl 0344. 35036.
14. E. Giusti, "On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions", Invent. Math. 46:2 (1978), 111-137. MR 58 #7337 Zbl 0381.35035.
15. E. Gonzalez, U. Massari, and I. Tamanini, "On the regularity of boundaries of sets minimizing perimeter with a volume constraint", Indiana Univ. Math. J. 32:1 (1983), 25-37. MR 84d:49043 Zbl 0486.49024.
16. B. Kawohl and N. Kutev, "Global behaviour of solutions to a parabolic mean curvature equation", Differential Integral Equations 8:8 (1995), 1923-1946. MR 96f:35088 Zbl 0844.35050.
17. B. Kawohl and T. Lachand-Robert, "Characterization of Cheeger sets for convex subsets of the plane", Pacific J. Math. 225:1 (2006), 103-118. MR 2007e:52002 Zbl 05170768.
18. B. Kawohl and M. Novaga, "The p-Laplace eigenvalue problem as p → 1 and Cheeger sets in a Finsler metric", preprint, 2006, Available http://cvgmt.sns.it/papers/kawnov06/KawNovFeb27.pdf.
19. A. Lichnewsky and R. Temam, "Pseudosolutions of the time-dependent minimal surface problem", J. Differential Equations 30:3 (1978), 340-364. MR 80a:35059 Zbl 0368.49016.
20. E. Stredulinsky and W. P. Ziemer, "Area minimizing sets subject to a volume constraint in a convex set", J. Geom. Anal. 7:4 (1997), 653-677. MR 99k:49089 Zbl 0940.49025.