Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 13
Number of page(s) 23
DOI https://doi.org/10.1051/cocv/2023001
Published online 25 January 2023
  1. M. Amar, V. De Cicco and N. Fusco, Lower semicontinuity results for free discontinuity energies. Math. Models Methods Appl. Sci. 20 (2010) 707–730. [Google Scholar]
  2. L. Ambrosio, On the lower semicontinuity of quasi-convex integrals in SBV(Ω; ℝk). Nonlinear Anal. 23 (1994) 405–425. [Google Scholar]
  3. L. Ambrosio and A. Braides, Functionals defined on partitions in sets of finite perimeter II: semicontinuity, relaxation and homogenization. J. Math. Pures Appl. 69 (1990) 307–333. [Google Scholar]
  4. L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Ratl. Mech. Anal., 139 (1997) 201–238. [Google Scholar]
  5. L. Ambrosio, G. Crasta, V. De Cicco and G. De Philippis, A nonautonomous chain rule formula in W1,p and in BV. Manuscr. Math. 140 (2013) 461–480. [Google Scholar]
  6. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Monographs, The Clarendon Press Oxford University Press, New York (2000). [Google Scholar]
  7. G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7 (1962) 55–129. [Google Scholar]
  8. G. Bellettini, A. Coscia and G. Dal Maso, Compactness and lower semicontinuity properties in SBD(Ω). Math. Z. 228 (1998) 337–351. [Google Scholar]
  9. M. Carriero, G. Dal Maso, A. Leaci and E. Pascali, Relaxation of the non-parametric Plateau problem with an obstacle. J. Math. Pures Appl. 67 (1988) 359–396. [Google Scholar]
  10. C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math. 580. Springer Verlag, Berlin (1977). [Google Scholar]
  11. A. Chambolle, S. Conti and F. Iurlano, Approximation of functions with small jump sets and existence of strong minimizers of Griffith’s energy. J. Math. Pures Appl. 128 (2019), 119–139. [Google Scholar]
  12. A. Chambolle and V. Crismale, A density result in GSBDp with applications to the approximation of brittle fracture energies. Arch. Ratl. Mech. Anal. 232 (2019) 1329–1378. [Google Scholar]
  13. A. Chambolle and V. Crismale, Compactness and lower semicontinuity in GSBD. J. Eur. Math. Soc. 23 (2021) 701–719. [Google Scholar]
  14. A. Chambolle and V. Crismale, Equilibrium configurations for nonhomogeneous linearly elastic materials with surface discontinuities. To appear on Ann. Sc. Norm. Super. Pisa Cl. Sci. (2022). D0I:10.2422/2036-2145.202006_002. [Google Scholar]
  15. S. Conti, M. Focardi and F. Iurlano, Existence of strong minimizers for the Griffith static fracture model in dimension two. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019) 455–474. [Google Scholar]
  16. V. Crismale, On the approximation of SBD functions and some applications. SIAM J. Math. Anal. 51 (2019) 5011–5048. [Google Scholar]
  17. V. Crismale and M. Friedrich, Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity. Arch. Ratl. Mech. Anal. 237 (2020) 1041–1098. [Google Scholar]
  18. G. Dal Maso, On the integral representation of certain local functionals. Ricerche Mat. 32 (1983) 85–113. [Google Scholar]
  19. G. Dal Maso, Generalised functions of bounded deformation. J. Eur. Math. Soc. 15 (2013) 1943–1997. [Google Scholar]
  20. G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165–225. [Google Scholar]
  21. G. Dal Maso, G. Orlando and R. Toader, Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation. Adv. Calc. Var. 10 (2017) 183–207. [Google Scholar]
  22. G. Dal Maso and R. Toader, A model for the quasistatic growth of brittle fractures, existence and approximation results. Arch. Ratl. Mech. Anal. 162 (2002) 101–135. [Google Scholar]
  23. V. De Cicco, Lower semicontinuity for nonautonomous surface integrals. Rend. Lincei Mat. Appl. 26 (2015) 1–21. [Google Scholar]
  24. V. De Cicco, N. Fusco and A. Verde, A chain rule formula in BV and application to lower semicontinuity. Calc. Var. 28 (2007) 427–447. [Google Scholar]
  25. V. De Cicco, N. Fusco and A. Verde, On L1-lower semicontinuity in BV. J. Convex Anal. 12 (2005) 173–185. [Google Scholar]
  26. E. De Giorgi, Semicontinuity theorems in the calculus of variations. With notes by U. Mosco, G. Troianiello and G. Vergara and a preface by C. Sbordone. Quaderni dell’Accademia Pontaniana 56 (2008). [Google Scholar]
  27. F. Ebobisse, A lower semicontinuity result for some integral functionals in the space SBD. Nonlinear Anal: Theory, Methods Appl. A 62 (2005) 1333–1351. [Google Scholar]
  28. H. Federer and W.P. Ziemer, The Lebesgue set of a function whose distribution derivatives are pth power summable. Indiana Un. Math. J. 22 (1972) 139–158. [Google Scholar]
  29. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces. Springer Monographs in Mathematics, Springer (2007). [Google Scholar]
  30. G.A. Francfort and J.J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [Google Scholar]
  31. M. Friedrich, M. Perugini and F. Solombrino, Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD. J. Funct. Anal. 280 (2021) 108929. [Google Scholar]
  32. M. Friedrich and F. Solombrino, Functionals defined on piecewise rigid functions: integral representation and Γ-convergence. Arch. Ratl. Mech. Anal. 236 (2020) 1325–1387. [Google Scholar]
  33. M. Friedrich and F. Solombrino, Quasistatic crack growth in 2d-linearized elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018) 27–64. [Google Scholar]
  34. G. Gargiulo and E. Zappale, A lower semicontinuity result in SBD. J. Convex Anal. 15 (2008) 191–200. [Google Scholar]
  35. G. Gargiulo and E. Zappale, Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics. Math. Methods Appl. Sci. 34 (2011) 1541–1552. [Google Scholar]
  36. A.A. Griffith, The phenomenon of rupture and flow in solids. Phil Trans. Royal Soc. London A 221 (1920) 163–198. [Google Scholar]
  37. S.Y. Kholmatov and P. Piovano, A unified model for stress-driven rearrangement instabilities. Arch. Ratl. Mech. Anal. 238 (2020) 415–488. [Google Scholar]
  38. R. Temam, Mathematical problems in plasticity. Gauthier-Villars (1985). [Google Scholar]

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