A characterization of convex calibrable sets in R N with respect to anisotropic norms

V. Caselles; A. Chambolle; S. Moll; M. Novaga

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 4, page 803-832
  • ISSN: 0294-1449

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Caselles, V., et al. "A characterization of convex calibrable sets in ${R}^{N}$ with respect to anisotropic norms." Annales de l'I.H.P. Analyse non linéaire 25.4 (2008): 803-832. <http://eudml.org/doc/78812>.

@article{Caselles2008,
author = {Caselles, V., Chambolle, A., Moll, S., Novaga, M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {calibrable sets; convex sets; mean curvature; total variation},
language = {eng},
number = {4},
pages = {803-832},
publisher = {Elsevier},
title = {A characterization of convex calibrable sets in $\{R\}^\{N\}$ with respect to anisotropic norms},
url = {http://eudml.org/doc/78812},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Caselles, V.
AU - Chambolle, A.
AU - Moll, S.
AU - Novaga, M.
TI - A characterization of convex calibrable sets in ${R}^{N}$ with respect to anisotropic norms
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 4
SP - 803
EP - 832
LA - eng
KW - calibrable sets; convex sets; mean curvature; total variation
UR - http://eudml.org/doc/78812
ER -

References

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  1. [1] F. Alter, V. Caselles, Uniqueness of the Cheeger set of a convex body, Preprint CVGMT, Scuola Normale di Pisa, 2007. Zbl1167.52005MR2358032
  2. [2] Alter F., Caselles V., Chambolle A., A characterization of convex calibrable sets in R N , Math. Ann.332 (2) (2005) 329-366. Zbl1108.35073MR2178065
  3. [3] Alter F., Caselles V., Chambolle A., Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow, Interfaces Free Bound.7 (1) (2005) 29-53. Zbl1084.49003MR2126142
  4. [4] Amar M., Bellettini G., A notion of total variation depending on a metric with discontinuous coefficients, Ann. Inst. H. Poincaré Anal. Non Linéaire11 (1) (1994) 91-133. Zbl0842.49016MR1259102
  5. [5] Ambrosio L., Movimenti minimizzanti, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5)19 (1995) 191-246. Zbl0957.49029MR1387558
  6. [6] Ambrosio L., Fusco N., Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2000. Zbl0957.49001MR1857292
  7. [7] Andreu F., Ballester C., Caselles V., Mazón J.M., The Dirichlet problem for the total variation flow, J. Funct. Anal.180 (2) (2001) 347-403. Zbl0973.35109MR1814993
  8. [8] Andreu F., Caselles V., Mazón J.M., A parabolic quasilinear problem for linear growth functionals, Rev. Mat. Iberoamericana18 (1) (2002) 135-185. Zbl1010.35063MR1924690
  9. [9] Andreu-Vaillo F., Caselles V., Mazón J.M., Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, Progress in Mathematics, vol. 223, Birkhäuser Verlag, Basel, 2004. Zbl1053.35002MR2033382
  10. [10] Anzellotti G., Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4)135 (1984) 293-318, 1983. Zbl0572.46023MR750538
  11. [11] Atkinson F.V., Peletier L.A., Bounds for vertical points of solutions of prescribed mean curvature type equations. I, Proc. Roy. Soc. Edinburgh Sect. A112 (1–2) (1989) 15-32. Zbl0685.35022MR1007535
  12. [12] Barozzi E., The curvature of a set with finite area, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.5 (2) (1994) 149-159. Zbl0809.49038MR1292570
  13. [13] Bellettini G., Caselles V., Chambolle A., Novaga M., Crystalline mean curvature flow of convex sets, Arch. Ration. Mech. Anal.179 (1) (2006) 109-152. Zbl1148.53049MR2208291
  14. [14] Bellettini G., Caselles V., Novaga M., The total variation flow in R N , J. Differential Equations184 (2) (2002) 475-525. Zbl1036.35099MR1929886
  15. [15] Bellettini G., Novaga M., Approximation and comparison for nonsmooth anisotropic motion by mean curvature in R N , Math. Models Methods Appl. Sci.10 (1) (2000) 1-10. Zbl1016.53048MR1749692
  16. [16] Bellettini G., Novaga M., Paolini M., Facet-breaking for three-dimensional crystals evolving by mean curvature, Interfaces Free Bound.1 (1) (1999) 39-55. Zbl0934.49023MR1865105
  17. [17] Bellettini G., Novaga M., Paolini M., Characterization of facet breaking for nonsmooth mean curvature flow in the convex case, Interfaces Free Bound.3 (4) (2001) 415-446. Zbl0989.35127MR1869587
  18. [18] Bellettini G., Novaga M., Paolini M., On a crystalline variational problem. I. First variation and global L regularity, Arch. Ration. Mech. Anal.157 (3) (2001) 165-191. Zbl0976.58016MR1826964
  19. [19] Bellettini G., Novaga M., Paolini M., On a crystalline variational problem. II. BV regularity and structure of minimizers on facets, Arch. Ration. Mech. Anal.157 (3) (2001) 193-217. Zbl0976.58017MR1826965
  20. [20] Bellettini G., Paolini M., Anisotropic motion by mean curvature in the context of Finsler geometry, Hokkaido Math. J.25 (3) (1996) 537-566. Zbl0873.53011MR1416006
  21. [21] Brézis H., Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, vol. 5, North-Holland Publishing Co., Amsterdam, 1973, Notas de Matemática (50). Zbl0252.47055MR348562
  22. [22] Brézis H., Kinderlehrer D., The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J.23 (1973/1974) 831-844. Zbl0278.49011MR361436
  23. [23] Caselles V., Chambolle A., Anisotropic curvature-driven flow of convex sets, Nonlinear Anal.65 (8) (2006) 1547-1577. Zbl1107.35069MR2248685
  24. [24] Caselles V., Chambolle A., Novaga M., Uniqueness of the Cheeger set of a convex body, Pacific J. Math.232 (1) (2007) 77-90. Zbl1221.35171MR2358032
  25. [25] Chambolle A., An algorithm for mean curvature motion, Interfaces Free Bound.6 (2) (2004) 195-218. Zbl1061.35147MR2079603
  26. [26] Chambolle A., An algorithm for total variation minimization and applications, J. Math. Imaging Vision20 (1–2) (2004) 89-97, Special issue on mathematics and image analysis. MR2049783
  27. [27] Giusti E., On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions, Invent. Math.46 (2) (1978) 111-137. Zbl0381.35035MR487722
  28. [28] Gonzalez E.H.A., Massari U., Variational mean curvatures, Rend. Sem. Mat. Univ. Politec. Torino52 (1) (1994) 1-28. Zbl0819.49025MR1289900
  29. [29] Kawohl B., Fridman V., Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolin.44 (4) (2003) 659-667. Zbl1105.35029MR2062882
  30. [30] Kawohl B., Lachand-Robert T., Characterization of Cheeger sets for convex subsets of the plane, Pacific J. Math.225 (1) (2006) 103-118. Zbl1133.52002MR2233727
  31. [31] Korevaar N., Capillary surface convexity above convex domains, Indiana Univ. Math. J.32 (1) (1983) 73-81. Zbl0481.35023MR684757
  32. [32] Korevaar N., Simon L., Equations of mean curvature type with contact angle boundary conditions, in: Geometric Analysis and the Calculus of Variations, Internat. Press, Cambridge, MA, 1996, pp. 175-201. Zbl0932.35091MR1449407
  33. [33] Lichnewsky A., Temam R., Pseudosolutions of the time-dependent minimal surface problem, J. Differential Equations30 (3) (1978) 340-364. Zbl0368.49016MR521858
  34. [34] Meyer Y., Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, vol. 22, American Mathematical Society, Providence, RI, 2001, The fifteenth Dean Jacqueline B. Lewis memorial lectures. Zbl0987.35003MR1852741
  35. [35] Moll J.S., The anisotropic total variation flow, Math. Ann.332 (1) (2005) 177-218. Zbl1109.35061MR2139257
  36. [36] Rosales C., Isoperimetric regions in rotationally symmetric convex bodies, Indiana Univ. Math. J.52 (5) (2003) 1201-1214. Zbl1088.53039MR2010323
  37. [37] Schneider R., Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. Zbl0798.52001MR1216521
  38. [38] Simon L., Spruck J., Existence and regularity of a capillary surface with prescribed contact angle, Arch. Ration. Mech. Anal.61 (1) (1976) 19-34. Zbl0361.35014MR487724
  39. [39] Stredulinsky E., Ziemer W.P., Area minimizing sets subject to a volume constraint in a convex set, J. Geom. Anal.7 (4) (1997) 653-677. Zbl0940.49025MR1669207

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