Regularity of minimizers for a class of membrane energies

Emilio Acerbi; Irene Fonseca; Nicola Fusco[1]

  • [1] Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 25, Issue: 1-2, page 11-25
  • ISSN: 0391-173X

How to cite

top

Acerbi, Emilio, Fonseca, Irene, and Fusco, Nicola. "Regularity of minimizers for a class of membrane energies." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.1-2 (1997): 11-25. <http://eudml.org/doc/84280>.

@article{Acerbi1997,
affiliation = {Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;},
author = {Acerbi, Emilio, Fonseca, Irene, Fusco, Nicola},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {SBV; functions of special bounded variation; Mumford-Shah functional; regularity; free discontinuity sets; local minimizers},
language = {eng},
number = {1-2},
pages = {11-25},
publisher = {Scuola normale superiore},
title = {Regularity of minimizers for a class of membrane energies},
url = {http://eudml.org/doc/84280},
volume = {25},
year = {1997},
}

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
PB - Scuola normale superiore
VL - 25
IS - 1-2
SP - 11
EP - 25
LA - eng
KW - SBV; functions of special bounded variation; Mumford-Shah functional; regularity; free discontinuity sets; local minimizers
UR - http://eudml.org/doc/84280
ER -

References

top
  1. [1] E. Acerbi - I. Fonseca - N. Fusco, Regularity results for equilibria in a variational model for fracture, to appear in Proc. R. Soc. Edin. Zbl0895.73080MR1475635
  2. [2] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital. B3 (1989), 857-881. Zbl0767.49001MR1032614
  3. [3] L. Ambrosio, A new proof of the SBV compactness theorem, Calc. Var.3 (1995), 127-137. Zbl0837.49011MR1384840
  4. [4] L. Ambrosio, On the lower semicontinuity of quasiconvex integrals in S B V (Ω, Rk), Nonlinear Anal., 23 (1994), 405-425. Zbl0817.49017
  5. [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. Zbl0896.49024MR1475772
  6. [6] L. Ambrosio - D. Pallara, Partial regularity of free discontinuity sets I., Ann. Scuola Norm. Sup. Pisa Cl. Sci.24 (1997), 1-38. Zbl0896.49023MR1475771
  7. [7] K. Bhattacharya - R. James, in preparation. 
  8. [8] P. Bauman - N.C. Owen - D. Phillips, Maximum principles and apriori estimates for a class of problems from nonlinear elasticity, Ann. Inst. H. Poincaré8 (1991), 119-157. Zbl0733.35015MR1096601
  9. [9] A. Blake - A. Zissermann, "Visual Reconstruction", The MIT Press, Cambridge, Massachussets, 1985. MR919733
  10. [10] A. Bonnet, On the regularity of edges in the Mumford-Shah model for image segmentation, Ann. Inst. H. Poincaré, Anal. Non Linéaire13 (1996), 485-528. Zbl0883.49004MR1404319
  11. [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. Zbl0753.49018MR1145314
  12. [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. Zbl0405.73050MR533827
  13. [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. Zbl0853.49010MR1411155
  14. [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. Zbl0758.49002MR1110593
  15. [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. Zbl0715.49014MR1152641
  16. [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. Zbl0682.49002MR1012174
  17. [17] M. Dougherty, Higher integrability of the gradient for minimizers of certain polyconvex functionals in the calculus of variations, preprint. 
  18. [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. Zbl0847.73077MR1385294
  19. [19] I. Fonseca - G. Francofort, Optimal design problems in elastic membranes, to appear. 
  20. [20] I. Fonseca - N. Fusco, Regularity results for anisotropic image segmentation models, Ann. Scuola Norm. Sup. Pisa Cl. Sci.24 (1997), 463-499. Zbl0899.49018MR1612389
  21. [21] M. Giaquinta, "Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems", Annals of Mathematics Studies, Princeton University Press, 1983. Zbl0516.49003MR717034
  22. [22] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Berlin, 1983. Zbl0562.35001MR737190
  23. [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. Zbl0847.73025MR1365259
  24. [24] C.B. Morrey, "Multiple integrals in the Calculus of Variations", Springer, Berlin1966. Zbl0142.38701
  25. [25] D. Mumford - J. Shah, Boundary detection by minimizing functionals, Proc. IEEE Conf. on "Computer Vision and Pattern Recognition", San Francisco, 1985. 

NotesEmbed ?

top

You must be logged in to post comments.