Some remarks on uniqueness and regularity of Cheeger sets

Caselles, V.; Chambolle, A.; Novaga, M.

Caselles, V. ; Chambolle, A. ; Novaga, M.

Rendiconti del Seminario Matematico della Università di Padova, Tome 123 (2010), pp. 191-202.

MR Zbl | 2 citations dans Numdam

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     author = {Caselles, V. and Chambolle, A. and Novaga, M.},
     title = {Some remarks on uniqueness and regularity of {Cheeger} sets},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {191--202},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {123},
     year = {2010},
     mrnumber = {2683297},
     zbl = {1198.49042},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2010__123__191_0/}
}

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Caselles, V.; Chambolle, A.; Novaga, M. Some remarks on uniqueness and regularity of Cheeger sets. Rendiconti del Seminario Matematico della Università di Padova, Tome 123 (2010), pp. 191-202. http://www.numdam.org/item/RSMUP_2010__123__191_0/

Bibliographie
Cité par

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

[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 | Zbl

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

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

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

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

[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

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

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

[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 | Zbl

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

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

[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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[24] B. Kawohl - M. Novaga, The $p$ -Laplace eigenvalue problem as $p \to 1$ and Cheeger sets in a Finsler metric, J. Convex Anal., 15 (3) (2008), pp. 623--634. | MR | Zbl

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

[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 | Zbl

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

[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 | Zbl

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