Regularity of minimizers for a class of membrane energies
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 25 (1997) no. 1-2, p. 11-25
@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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {1-2},
     year = {1997},
     pages = {11-25},
     zbl = {1015.49011},
     mrnumber = {1655507},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 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 1475635 | Zbl 0895.73080

[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 1032614 | Zbl 0767.49001

[3] L. Ambrosio, A new proof of the SBV compactness theorem, Calc. Var. 3 (1995), 127-137. | MR 1384840 | Zbl 0837.49011

[4] L. Ambrosio, On the lower semicontinuity of quasiconvex integrals in S B V (Ω, Rk), Nonlinear Anal., 23 (1994), 405-425. | Zbl 0817.49017

[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. | Numdam | MR 1475772 | Zbl 0896.49024

[6] L. Ambrosio - D. Pallara, Partial regularity of free discontinuity sets I., Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997), 1-38. | Numdam | MR 1475771 | Zbl 0896.49023

[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. | Numdam | MR 1096601 | Zbl 0733.35015

[9] A. Blake - A. Zissermann, "Visual Reconstruction", The MIT Press, Cambridge, Massachussets, 1985. | MR 919733

[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 1404319 | Zbl 0883.49004

[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 1145314 | Zbl 0753.49018

[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 533827 | Zbl 0405.73050

[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 1411155 | Zbl 0853.49010

[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 1110593 | Zbl 0758.49002

[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 1152641 | Zbl 0715.49014

[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 1012174 | Zbl 0682.49002

[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 1385294 | Zbl 0847.73077

[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 1612389 | Zbl 0899.49018

[21] M. Giaquinta, "Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems", Annals of Mathematics Studies, Princeton University Press, 1983. | MR 717034 | Zbl 0516.49003

[22] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[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 1365259 | Zbl 0847.73025

[24] C.B. Morrey, "Multiple integrals in the Calculus of Variations", Springer, Berlin 1966. | Zbl 0142.38701

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