Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme
Mémoires de la Société Mathématique de France, no. 82 (2000) , 110 p.
@book{MSMF_2000_2_82__R1_0,
     author = {Rigot, S\'everine},
     title = {Ensembles quasi-minimaux avec contrainte de volume et rectifiabilit\'e uniforme},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {82},
     year = {2000},
     doi = {10.24033/msmf.395},
     mrnumber = {2002j:49053},
     zbl = {0983.49025},
     language = {fr},
     url = {http://www.numdam.org/item/MSMF_2000_2_82__R1_0/}
}
TY  - BOOK
AU  - Rigot, Séverine
TI  - Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme
T3  - Mémoires de la Société Mathématique de France
PY  - 2000
IS  - 82
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/MSMF_2000_2_82__R1_0/
DO  - 10.24033/msmf.395
LA  - fr
ID  - MSMF_2000_2_82__R1_0
ER  - 
%0 Book
%A Rigot, Séverine
%T Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme
%S Mémoires de la Société Mathématique de France
%D 2000
%N 82
%I Société mathématique de France
%U http://www.numdam.org/item/MSMF_2000_2_82__R1_0/
%R 10.24033/msmf.395
%G fr
%F MSMF_2000_2_82__R1_0
Rigot, Séverine. Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme. Mémoires de la Société Mathématique de France, Série 2, no. 82 (2000), 110 p. doi : 10.24033/msmf.395. http://numdam.org/item/MSMF_2000_2_82__R1_0/

[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. | Zbl | MR

[AP99] L. Ambrosio & E. Paolini - "Partial regularity for quasi minimizers of perimeter", Ricerche Mat. 48 (1999), p. 167-186. | Zbl | MR

[DG61] E. De Giorgi - "Frontiere orientale di misura minima", Sem. Mat. Scuola Norm. Sup. Pisa, 1960-1961.

[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. | Zbl | MR

[DS91] G. David & S. Semmes - "Singular integrals and rectifiable sets in ℝn : Beyond Lipschitz Graphs", Astérisque (1991), no. 193. | Zbl | MR | Numdam

[DS93a] G. David & S. Semmes - Analysis of and on uniformly rectifiable sets, Math. Surveys Monogr., vol. 38, Amer. Math. Soc., Providence, 1993. | Zbl | MR

[DS93b] G. David & S. Semmes - "Quantitative rectifiability and Lipschitz mappings", Trans. Amer. Math. Soc. 337 (1993), no. 2, p. 855-889. | Zbl | MR

[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. | Zbl | MR

[DS96b] G. David & S. Semmes - "Uniform rectifiability and singular sets", Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 4, p. 383-443. | Zbl | MR | Numdam

[DS98] G. David & S. Semmes, "Quasiminimal surfaces of codimension 1 and John domains", Pacific J. Math. 183 (1998), no. 2, p. 213-277. | Zbl | MR

[DS00] G. David & S. Semmes, "Uniform rectifiability and quasiminimizing sets of arbitrary codimension", Mem. Amer. Math. Soc. 144 (2000), no. 687. | Zbl | MR

[EG92] L. Evans & R. Gariepy - Measure theory and fine properties of functions, CRC Press, 1992. | Zbl | MR

[Fed69] H. Federer - Geometric measure theory, Springer-Verlag, Berlin, 1969. | Zbl | MR

[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. | Zbl | MR

[Giu81] E. Giusti - "The equilibrium configuration of liquid drops", J. Reine Angew. Math. 321 (1981), p. 53-63. | Zbl | MR

[Giu84] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Basel-Boston, 1984. | Zbl | MR

[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. | Zbl | MR

[Mas74] U. Massari - "Esistenza e regolarità delle ipersuperfice di curvatura media assegnata in ℝn", Arch. Rational Mech. Anal 55 (1974), p. 357-382. | Zbl | MR

[Mas75] U. Massari, "Frontiere orientale di curvatura media assegnata in Lp", Rend. Sem. Mat. Univ. Padova 53 (1975), p. 37-52. | Zbl | MR | Numdam

[Mat95] P. Mattila - Geometry of sets and measures in Euclidean spaces, Cambridge University Press, Cambridge, 1995. | Zbl | MR

[Mir65] M. Miranda - "Sul minimo dell'integrale del gradiente di una funzione", Ann. Scuola Norm. Sup. Pisa (3) 19 (1965), p. 626-665. | Zbl | MR | Numdam

[MM84] U. Massari & M. Miranda - Minimal surfaces of codimension 1, North Holland, Amsterdam-New York, 1984. | Zbl | MR

[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. | Zbl | MR

[Rig00] S. Rigot - "Uniform partial regularity of quasi minimizers for the perimeter", Cal. Var. Partial Differential Equations 10 (2000), no. 4, p. 389-406. | Zbl | MR

[Sim83] L. Simon - Lectures on Geometric Measure Theory, Proc. C.M.A., 1983. | Zbl | MR

[Sol97] S. Solimini - "Simplified excision techniques for free discontinuity problems in several variables", J. Funct. Anal. 151 (1997), no. 1, p. 1-34. | Zbl | MR

[Tam82] I. Tamanini - "Boundaries of Caccioppoli sets with Hölder continuous normal vector", J. Reine Angew. Math. 334 (1982), p. 27-39. | Zbl | MR

[Tam84] I. Tamanini, Regularity results for almost minimal oriented hypersurfaces in ℝn, Quaderni Del Dipartimento Di Matematica Dell' Universita' Di Lecce, 1984.

[Zie89] W. P. Ziemer - Weakly differentiable functions, Springer-Verlag, Berlin, 1989. | Zbl | MR

Cité par Sources :