Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme

Séverine Rigot

Mémoires de la Société Mathématique de France (2000)

  • Volume: 82, page I1-VI104
  • ISSN: 0249-633X

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Rigot, Séverine. "Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme." Mémoires de la Société Mathématique de France 82 (2000): I1-VI104. <http://eudml.org/doc/94933>.

@article{Rigot2000,
author = {Rigot, Séverine},
journal = {Mémoires de la Société Mathématique de France},
keywords = {Ahlfors regularity; uniform rectifiability; quasi-minimum perimeter; uniform estimations; volume constraint},
language = {fre},
pages = {I1-VI104},
publisher = {Société mathématique de France},
title = {Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme},
url = {http://eudml.org/doc/94933},
volume = {82},
year = {2000},
}

TY - JOUR
AU - Rigot, Séverine
TI - Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme
JO - Mémoires de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 82
SP - I1
EP - VI104
LA - fre
KW - Ahlfors regularity; uniform rectifiability; quasi-minimum perimeter; uniform estimations; volume constraint
UR - http://eudml.org/doc/94933
ER -

References

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  1. [Alm76] F. J. ALMGREN — "Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints", Mem. Amer. Math. Soc. 4 (1976), no. 165. Zbl0327.49043MR54 #8420
  2. [AP99] L. AMBROSIO & E. PAOLINI — "Partial regularity for quasi minimizers of perimeter", Ricerche Mat. 48 (1999), p. 167-186. Zbl0943.49032MR2001g:49057
  3. [DG61] E. DE GIORGI — "Frontiere orientale di misura minima", Sem. Mat. Scuola Norm. Sup. Pisa, 1960-1961. 
  4. [DMS92] G. DAL MASO, J.-M. MOREL & S. SOLIMINI — "A variational method in image segmentation : existence and approximation results", Acta Math. 168 (1992), no. 1-2, p. 89-151. Zbl0772.49006MR92m:49020
  5. [DS91] G. DAVID & S. SEMMES — "Singular integrals and rectifiable sets in ℝn : Beyond Lipschitz Graphs", Astérisque (1991), no. 193. Zbl0743.49018MR92j:42016
  6. [DS93a] G. DAVID & S. SEMMES — Analysis of and on uniformly rectifiable sets, Math. Surveys Monogr., vol. 38, Amer. Math. Soc., Providence, 1993. Zbl0832.42008MR94i:28003
  7. [DS93b] G. DAVID & S. SEMMES — "Quantitative rectifiability and Lipschitz mappings", Trans. Amer. Math. Soc. 337 (1993), no. 2, p. 855-889. Zbl0792.49029MR93h:42015
  8. [DS96a] G. DAVID & S. SEMMES — "On the singular sets of minimizers of the Mumford-Shah functional", J. Math. Pures Appl. (9) 75 (1996), no. 4, p. 299-342. Zbl0853.49010MR98a:49068
  9. [DS96b] G. DAVID & S. SEMMES — "Uniform rectifiability and singular sets", Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 4, p. 383-443. Zbl0908.49030MR98a:49067
  10. [DS98] G. DAVID & S. SEMMES, "Quasiminimal surfaces of codimension 1 and John domains", Pacific J. Math. 183 (1998), no. 2, p. 213-277. Zbl0921.49031MR99i:28012
  11. [DS00] G. DAVID & S. SEMMES, "Uniform rectifiability and quasiminimizing sets of arbitrary codimension", Mem. Amer. Math. Soc. 144 (2000), no. 687. Zbl0966.49024MR2000i:49062
  12. [EG92] L. EVANS & R. GARIEPY — Measure theory and fine properties of functions, CRC Press, 1992. Zbl0804.28001MR93f:28001
  13. [Fed69] H. FEDERER — Geometric measure theory, Springer-Verlag, Berlin, 1969. Zbl0176.00801MR41 #1976
  14. [Fed70] H. FEDERER, "The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension", Bull. Amer. Math. Soc. 76 (1970), p. 767-771. Zbl0194.35803MR41 #5601
  15. [Giu81] E. GIUSTI — "The equilibrium configuration of liquid drops", J. Reine Angew. Math. 321 (1981), p. 53-63. Zbl0438.76078MR82c:49037
  16. [Giu84] E. GIUSTI, Minimal surfaces and functions of bounded variation, Birkhäuser, Basel-Boston, 1984. Zbl0545.49018MR87a:58041
  17. [GMT83] E. GONZALEZ, U. MASSARI & I. TAMANINI — "On the regularity of boundaries of sets minimizing perimeter with a volume constraint", Indiana Univ. Math. J. 32 (1983), no. 1, p. 25-37. Zbl0486.49024MR84d:49043
  18. [Mas74] U. MASSARI — "Esistenza e regolarità delle ipersuperfice di curvatura media assegnata in ℝn", Arch. Rational Mech. Anal 55 (1974), p. 357-382. Zbl0305.49047MR50 #8240
  19. [Mas75] U. MASSARI, "Frontiere orientale di curvatura media assegnata in Lp", Rend. Sem. Mat. Univ. Padova 53 (1975), p. 37-52. Zbl0358.49019MR54 #5953
  20. [Mat95] P. MATTILA — Geometry of sets and measures in Euclidean spaces, Cambridge University Press, Cambridge, 1995. Zbl0819.28004MR96h:28006
  21. [Mir65] M. MIRANDA — "Sul minimo dell'integrale del gradiente di una funzione", Ann. Scuola Norm. Sup. Pisa (3) 19 (1965), p. 626-665. Zbl0166.09604MR32 #6271
  22. [MM84] U. MASSARI & M. MIRANDA — Minimal surfaces of codimension 1, North Holland, Amsterdam-New York, 1984. Zbl0565.49030MR87f:49058
  23. [Ott98] F. OTTO — "Dynamics of labyrinthine pattern formation in magnetic fluids : a mean-field theory", Arch. Rational Mech. Anal. 141 (1998), no. 1, p. 63-103. Zbl0905.35068MR2000j:76145
  24. [Rig00] S. RIGOT — "Uniform partial regularity of quasi minimizers for the perimeter", Cal. Var. Partial Differential Equations 10 (2000), no. 4, p. 389-406. Zbl0961.49025MR2001d:49061
  25. [Sim83] L. SIMON — Lectures on Geometric Measure Theory, Proc. C.M.A., 1983. Zbl0546.49019MR87a:49001
  26. [Sol97] S. SOLIMINI — "Simplified excision techniques for free discontinuity problems in several variables", J. Funct. Anal. 151 (1997), no. 1, p. 1-34. Zbl0891.49007MR98k:49056
  27. [Tam82] I. TAMANINI — "Boundaries of Caccioppoli sets with Hölder continuous normal vector", J. Reine Angew. Math. 334 (1982), p. 27-39. Zbl0479.49028MR83m:49067
  28. [Tam84] I. TAMANINI, Regularity results for almost minimal oriented hypersurfaces in ℝn, Quaderni Del Dipartimento Di Matematica Dell' Universita' Di Lecce, 1984. 
  29. [Zie89] W. P. ZIEMER — Weakly differentiable functions, Springer-Verlag, Berlin, 1989. Zbl0692.46022MR91e:46046

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