Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation

References

[1] Ambrosio L., Variational problems in SBV and image segmentation, Acta Appl. Math. 17 (1989), 1–40. 10.1007/BF00052492Search in Google Scholar

[2] Ambrosio L., Coscia A. and Dal Maso G., Fine properties of functions with bounded deformation, Arch. Ration. Mech. Anal. 139 (1997), 201–238. 10.1007/s002050050051Search in Google Scholar

[3] Ambrosio L., Fusco N. and Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Clarendon Press, Oxford, 2000. Search in Google Scholar

[4] Barroso A. C., Fonseca I. and Toader R., A relaxation theorem in the space of functions of bounded deformation, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 29 (2000), 19–49. Search in Google Scholar

[5] Bellettini G., Coscia A. and Dal Maso G., Compactness and lower semicontinuity properties in SBD(Ω), Math. Z. 228 (1998), 337–351. 10.1007/PL00004617Search in Google Scholar

[6] Bouchitté G., Braides A. and Buttazzo G., Relaxation results for some free discontinuity problems, J. Reine Angew. Math. 458 (1995), 1–18. Search in Google Scholar

[7] Bouchitté G. and Buttazzo G., New lower semicontinuity results for nonconvex functionals defined on measures, Nonlinear Anal. 15 (1990), 679–692. 10.1016/0362-546X(90)90007-4Search in Google Scholar

[8] Bouchitté G., Fonseca I., Leoni G. and Mascarenhas L., A global method for relaxation in W1,p and in SBVp, Arch. Ration. Mech. Anal. 165 (2002), 187–242. 10.1007/s00205-002-0220-ySearch in Google Scholar

[9] Bouchitté G., Fonseca I. and Mascarenhas L., A global method for relaxation, Arch. Ration. Mech. Anal. 145 (1998), 51–98. 10.1007/s002050050124Search in Google Scholar

[10] Bourdin B., Francfort G. A. and Marigo J.-J., The Variational Approach to Fracture, Springer, New York, 2008. 10.1007/978-1-4020-6395-4Search in Google Scholar

[11] Braides A., Γ-Convergence for Beginners, Oxford Lecture Ser. Math. Appl. 22, Oxford University Press, Oxford, 2002. 10.1093/acprof:oso/9780198507840.001.0001Search in Google Scholar

[12] Braides A. and Chiadò Piat V., Integral representation results for functionals defined on SBV(Ω;ℝm), J. Math. Pures Appl. (9) 75 (1996), 595–626. Search in Google Scholar

[13] Braides A. and De Cicco V., New lower semicontinuity and relaxation results for functionals defined on BV(Ω), Adv. Math. Sci. Appl. 6 (1996), 1–30. Search in Google Scholar

[14] Braides A., Defranceschi A. and Vitali E., Relaxation of elastic energies with free discontinuities and constraint on the strain, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002), 275–317. Search in Google Scholar

[15] Dal Maso G., An Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl. 8, Birkhäuser, Boston, 1993. 10.1007/978-1-4612-0327-8Search in Google Scholar

[16] De Giorgi E., Free discontinuity problems in calculus of variations, Frontiers in Pure and Applied Mathematics, North-Holland, Amsterdam (1991), 55–62. Search in Google Scholar

[17] Gargiulo G. and Zappale E., A lower semicontinuity result in SBD for surface integral functionals of fracture mechanics, Asymptot. Anal. 72 (2011), 231–249. 10.3233/ASY-2011-1032Search in Google Scholar

[18] Horn R. A. and Johnson C. R., Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, 2013. Search in Google Scholar

[19] Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities, 2nd ed., Birkhäuser, Basel, 2009. 10.1007/978-3-7643-8749-5Search in Google Scholar

[20] Morel J.-M. and Solimini S., Variational Methods in Image Segmentation, Progr. Nonlinear Differential Equations Appl. 14, Birkhäuser, Boston, 1995. 10.1007/978-1-4684-0567-5Search in Google Scholar

[21] Temam R., Problèmes mathématiques en plasticité, Méthodes Math. Inform. 12, Gauthier-Villars, Montrouge, 1983. Search in Google Scholar

[22] Virga E. G., Variational Theories for Liquid Crystals, Appl. Math. and Math. Comput. 8, Chapman & Hall, London, 1994. 10.1007/978-1-4899-2867-2Search in Google Scholar