no. 1-2
Regularity of minimizers for a class of membrane energies
Acerbi, Emilio ; Fonseca, Irene ; Fusco, Nicola1
1 Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 11-25.
Acerbi, Emilio  ; Fonseca, Irene  ; Fusco, Nicola 1

1 Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy; 
@article{ASNSP_1997_4_25_1-2_11_0,
     author = {Acerbi, Emilio and Fonseca, Irene and Fusco, Nicola},
     title = {Regularity of minimizers for a class of membrane energies},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {11--25},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {1-2},
     year = {1997},
     mrnumber = {1655507},
     zbl = {1015.49011},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_1-2_11_0/}
}
TY  - JOUR
AU  - Acerbi, Emilio
AU  - Fonseca, Irene
AU  - Fusco, Nicola
TI  - Regularity of minimizers for a class of membrane energies
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1997
SP  - 11
EP  - 25
VL  - 25
IS  - 1-2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1997_4_25_1-2_11_0/
LA  - en
ID  - ASNSP_1997_4_25_1-2_11_0
ER  - 
%0 Journal Article
%A Acerbi, Emilio
%A Fonseca, Irene
%A Fusco, Nicola
%T Regularity of minimizers for a class of membrane energies
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1997
%P 11-25
%V 25
%N 1-2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1997_4_25_1-2_11_0/
%G en
%F ASNSP_1997_4_25_1-2_11_0
Acerbi, Emilio; Fonseca, Irene; Fusco, Nicola. Regularity of minimizers for a class of membrane energies. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 11-25. http://www.numdam.org/item/ASNSP_1997_4_25_1-2_11_0/

[1] E. Acerbi - I. Fonseca - N. Fusco, Regularity results for equilibria in a variational model for fracture, to appear in Proc. R. Soc. Edin. | MR | Zbl

[2] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital. B 3 (1989), 857-881. | MR | Zbl

[3] L. Ambrosio, A new proof of the SBV compactness theorem, Calc. Var. 3 (1995), 127-137. | MR | Zbl

[4] L. Ambrosio, On the lower semicontinuity of quasiconvex integrals in S B V (Ω, Rk), Nonlinear Anal., 23 (1994), 405-425. | Zbl

[5] L. Ambrosio - N. Fusco - D. Pallara, Partial regularity of free discontinuity sets II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997) 39-62. | EuDML | Numdam | MR | Zbl

[6] L. Ambrosio - D. Pallara, Partial regularity of free discontinuity sets I., Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997), 1-38. | EuDML | Numdam | MR | Zbl

[7] K. Bhattacharya - R. James, in preparation.

[8] P. Bauman - N.C. Owen - D. Phillips, Maximum principles and apriori estimates for a class of problems from nonlinear elasticity, Ann. Inst. H. Poincaré 8 (1991), 119-157. | EuDML | Numdam | MR | Zbl

[9] A. Blake - A. Zissermann, "Visual Reconstruction", The MIT Press, Cambridge, Massachussets, 1985. | MR

[10] A. Bonnet, On the regularity of edges in the Mumford-Shah model for image segmentation, Ann. Inst. H. Poincaré, Anal. Non Linéaire 13 (1996), 485-528. | Numdam | MR | Zbl

[11] M. Carriero - A. Leaci, Sk-valued maps minimizing the Lp norm of the gradient with free discontinuities, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991), 321-352. | Numdam | MR | Zbl

[12] P.G. Ciarlet - P. Destuynder, A justification of a nonlinear model in plate theory, Comput. Methods Appl. Mech. Engrg.17/18 (1979), 227-258. | MR | Zbl

[13] G. David - S. Semmes, On the singular set of minimizers of the Mumford-Shah functional, J. Math. Pures et Appl. 75 (1996), 299-342. | MR | Zbl

[14] E. De Giorgi, Free Discontinuity Problems in the Calculus of Variations, a collection of papers dedicated to J. L. Lions on the occasion of his 60th birthday, North Holland (R. Dautray ed. ), 1991. | MR | Zbl

[15] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 82 (1988), 199-210. | MR | Zbl

[16] E. De Giorgi - M. Carriero - A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rat. Mech. Anal. 108 (1989), 195-218. | MR | Zbl

[17] M. Dougherty, Higher integrability of the gradient for minimizers of certain polyconvex functionals in the calculus of variations, preprint.

[18] I. Fonseca - G. Francofort, Relaxation in B V versus quasiconvexification in W1,p; a model for the interaction between fracture and damage, Calc. Var. 3 (1995), 407-446. | MR | Zbl

[19] I. Fonseca - G. Francofort, Optimal design problems in elastic membranes, to appear.

[20] I. Fonseca - N. Fusco, Regularity results for anisotropic image segmentation models, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997), 463-499. | Numdam | MR | Zbl

[21] M. Giaquinta, "Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems", Annals of Mathematics Studies, Princeton University Press, 1983. | MR | Zbl

[22] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Berlin, 1983. | MR | Zbl

[23] H. Le Dret - A. Raoult, The nonlinear membrane model as variational limit ofnonlinear three-dimensional elasticity, J. Math. Pures et Appl. 74 (1995), 549-578. | MR | Zbl

[24] C.B. Morrey, "Multiple integrals in the Calculus of Variations", Springer, Berlin 1966. | Zbl

[25] D. Mumford - J. Shah, Boundary detection by minimizing functionals, Proc. IEEE Conf. on "Computer Vision and Pattern Recognition", San Francisco, 1985.