Crack initiation in brittle materials

Archive for Rational Mechanics and Analysis

Volumn 188, Issue 2, 2008, Pages 309-349

  Chambolle, Antonin ^a   Giacomini, Alessandro ^b   Ponsiglione, Marcello ^c  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSITY OF BRESCIA   (Italy)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41149123496     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-007-0080-6     Document Type: Article

References (31)

1. Ambrosio L. (1989) A compactness theorem for a new class of functions of bounded variations. Boll. Un. Mat. Ital. 3-B: 857-881
2. Ambrosio L. (1990) Existence theory for a new class of variational problems. Arch. Ration. Mech. Anal. 111: 291-322
3. Ambrosio L. (1995) A new proof of the SBV compactness theorem. Calc. Var. Partial Differ. Equ. 3: 127-137
4. Ambrosio L., Fusco N., Pallara D. (2000) Functions of Bounded Variations and Free Discontinuity Problems. Clarendon, Oxford
5. Ambrosio L. Caselles V., Masnou S., Morel J.-M. (2001) Connected components of sets of finite perimeter and applications to image processing. J. Eur. Math. Soc. (JEMS) 3: 39-92
6. Astala K. (1994) Area distortion of quasiconformal mappings. Acta Math. 103(1): 37-60
7. Bonnetier E., Chambolle A. (2002) Computing the equilibrium configuration of epitaxially strained crystalline films. SIAM J. Appl. Math. 62:1093-1121
8. Boyarski B. (1955) Homeomorphic solutions of Beltrami systems (Russian). Dokl. Akad. Nauk SSSR (N.S) 102: 661-664
9. Boyarski B. (1957) Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients (Russian). Mat. Sb. N.S. 43(85): 451-503
10. Brezis, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam, 1973
11. 1,p estimates for elliptic equations in divergence form. Commun. Pure Appl. Math. 51: 1-21
12. Chambolle A. (2003) A density result in two-dimensional linearized elasticity, and applications. Arch. Ration. Mech. Anal. 167: 211-233
13. Dal Maso G., Morel J.-M., Solimini S. (1992) A variational method in image segmentation: existence and approximation results. Acta Math. 168(1-2): 89-151
14. Dal Maso G., Toader R. (2002) A model for the quasistatic growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal. 162: 101-135
15. Dal Maso G., Toader R. (2002) A model for the quasi-static growth of brittle fractures based on local minimization. Math. Models Methods Appl. Sci. 12: 1773-1799
16. David G. (2005) Singular Sets of Minimizers for the Mumford-Shah Functional. Progress in Mathematics. Birkhaüser, Basel
17. De Giorgi E., Carriero M., Leaci A. (1989) Existence theorem for a minimum problem with free discontinuity set. Arch Ration. Mech. Anal. 108: 195-218
18. Ebobisse F., Ponsiglione M. (2004) A duality approach for variational problems in domains with cracks. J. Convex Anal. 11: 17-40
19. Francfort G.A., Larsen C.J. (2003) Existence and convergence for quasistatic evolution in brittle fracture. Commun. Pure Appl. Math. 56: 1465-1500
20. Francfort G.A., Marigo J.-J. (1998) Revisiting brittle fractures as an energy minimization problem. J. Mech. Phys. Solids 46: 1319-1342
21. Grisvard P. (1985) Elliptic Problems in Nonsmooth Domains. Pitman, Boston
22. Leonetti F., Nesi V. (1997) Quasiconformal solutions to certain first order systems and the proof of a conjecture of G. W. Milton. J. Math. Pure Appl. 76: 109-124
23. Li Y., Nirenberg L. (2003) Estimates for elliptic systems from composite material. Dedicated to the memory of Jürgen K. Moser. Commun. Pure Appl. Math. 56: 892-925
24. Li Y., Vogelius M. (2000) Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Ration. Mech. Anal. 153: 91-151
25. Maddalena F., Solimini S. (2001) Lower semicontinuity properties of functionals with free discontinuities, Arch. Ration. Mech. Anal 159(4): 273-294
26. p -estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 17: 189-206
27. Mielke, A.: Analysis of energetic models for rate-independent materials. In: Proceedings of the International Congress of Mathematicians,Vol. III (Beijing, 2002), pp. 817-828, Higher Ed. Press, Beijing, 2002
28. Morel J.-M., Solimini S. (1995) Variational Methods in Image Segmentation. Birkhaüser, Boston
29. Mumford D., Shah J. (1989) Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42: 577-685
30. Rockafellar R.T. (1970) Convex Analysis. Princeton Mathematical Series, No. 28 Princeton University Press, Princeton
31. Solimini S. (1997) Simplified excision techniques for free discontinuity problems in several variables. J. Funct. Anal. 151: 1-34