{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T21:21:00Z","timestamp":1778275260914,"version":"3.51.4"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T00:00:00Z","timestamp":1422921600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Math Optim"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s00245-015-9289-1","type":"journal-article","created":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T01:47:04Z","timestamp":1422841624000},"page":"523-547","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Homogenization of Functionals with Linear Growth in the Context of $$\\mathcal A$$ A -quasiconvexity"],"prefix":"10.1007","volume":"72","author":[{"given":"Jos\u00e9","family":"Matias","sequence":"first","affiliation":[]},{"given":"Marco","family":"Morandotti","sequence":"additional","affiliation":[]},{"given":"Pedro M.","family":"Santos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,3]]},"reference":[{"key":"9289_CR1","doi-asserted-by":"crossref","first-page":"1482","DOI":"10.1137\/0523084","volume":"23","author":"G Allaire","year":"1992","unstructured":"Allaire, G.: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23, 1482\u20131518 (1992)","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"9289_CR2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1017\/S0308210500022757","volume":"126","author":"G Allaire","year":"1996","unstructured":"Allaire, G., Briane, M.: Multiscale convergence and reiterated homogenization. Proc. R. Soc. Edinb. Sect. A 126(2), 297\u2013342 (1996)","journal-title":"Proc. R. Soc. Edinb. Sect. A"},{"key":"9289_CR3","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/0022-1236(92)90012-8","volume":"109","author":"L Ambrosio","year":"1992","unstructured":"Ambrosio, L., Dal, G.: Maso: on the relaxation in $$BV(\\Omega; \\mathbb{R}^{m})$$ B V ( \u03a9 \u037e R m ) of quasi convex integrals. J. Funct. Anal. 109, 76\u201397 (1992)","journal-title":"J. Funct. Anal."},{"key":"9289_CR4","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of Bounded Variation and Free Discontinuity Problems","author":"L Ambrosio","year":"2000","unstructured":"Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000)"},{"key":"9289_CR5","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s00526-012-0524-1","volume":"47","author":"M Ba\u00eda","year":"2013","unstructured":"Ba\u00eda, M., Chermisi, M., Matias, J., Santos, P.M.: Lower semicontinuity and relaxation of signed functionals with linear growth in the context of $${\\cal A}$$ A -quasiconvexity. Calc. Var. Partial Differ. Equ. 47, 465\u2013498 (2013)","journal-title":"Calc. Var. Partial Differ. Equ."},{"key":"9289_CR6","first-page":"313","volume":"103","author":"A Braides","year":"1985","unstructured":"Braides, A.: Homogenization of some almost periodic functional. Rend. Accad. Naz. Sci. XL 103, 313\u2013322 (1985)","journal-title":"Rend. Accad. Naz. Sci. XL"},{"key":"9289_CR7","doi-asserted-by":"crossref","unstructured":"Braides, A.: $$\\Gamma $$ \u0393 -convergence for beginners. In: Oxford Lecture Series in Mathematics and its Applications, vol. 22. Oxford University Press, Oxford (2002). http:\/\/dx.doi.org\/10.1093\/acprof:oso\/9780198507840.001.0001","DOI":"10.1093\/acprof:oso\/9780198507840.001.0001"},{"key":"9289_CR8","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02198476","volume":"135","author":"A Braides","year":"1996","unstructured":"Braides, A., Defranceschi, A., Vitali, E.: Homogenization of free discontinuity problems. Arch. Rat. Mech. Anal. 135, 297\u2013356 (1996)","journal-title":"Arch. Rat. Mech. Anal."},{"key":"9289_CR9","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1051\/cocv:2000121","volume":"5","author":"A Braides","year":"2000","unstructured":"Braides, A., Fonseca, I., Leoni, G.: $${\\cal A}$$ A -quasiconvexity: relaxation and homogenization. ESAIM Control Optim. Calc. Var. 5, 539\u2013577 (2000). (electronic)","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"5","key":"9289_CR10","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1137\/040620898","volume":"37","author":"D Cioranescu","year":"2006","unstructured":"Cioranescu, D., Damlamian, A., De Arcangelis, R.: Homogenization of quasiconvex integrals via the periodic unfolding method. SIAM J. Math. Anal. 37(5), 1435\u20131453 (2006)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"9289_CR11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S1631-073X(02)02429-9","volume":"335","author":"D Cioranescu","year":"2002","unstructured":"Cioranescu, D., Damlamian, A., Griso, G.: Periodic unfolding and homogenization. C. R. Math. Acad. Sci. Paris 335(1), 99\u2013104 (2002)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"4","key":"9289_CR12","first-page":"585","volume":"40","author":"D Cioranescu","year":"2008","unstructured":"Cioranescu, D., Damlamian, A., Griso, G.: The periodic unfolding method in homogenization SIAM. J. Math. Anal. 40(4), 585\u20131620 (2008)","journal-title":"J. Math. Anal."},{"key":"9289_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0096144","volume-title":"Weak Continuity and Weak Lower Semicontinuity of Non-linear Functionals. Lecture Notes in Mathematics","author":"B Dacorogna","year":"1982","unstructured":"Dacorogna, B.: Weak Continuity and Weak Lower Semicontinuity of Non-linear Functionals. Lecture Notes in Mathematics. Springer, Berlin (1982)"},{"key":"9289_CR14","doi-asserted-by":"crossref","unstructured":"Dal Maso, G.: An introduction to $$\\Gamma $$ \u0393 -convergence. In: Progress in Nonlinear Differential Equations and their Applications, vol. 8. Birkh\u00e4user Boston Inc, Boston, MA (1993). http:\/\/dx.doi.org\/10.1007\/978-1-4612-0327-8","DOI":"10.1007\/978-1-4612-0327-8"},{"key":"9289_CR15","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/BF01261182","volume":"2","author":"R Arcangelis De","year":"1995","unstructured":"De Arcangelis, R., Gargiulo, G.: Homogenization of integral functionals with linear growth defined on vector-valued functions. NoDEA 2, 371\u2013416 (1995)","journal-title":"NoDEA"},{"key":"9289_CR16","first-page":"842","volume":"8","author":"E Giorgi De","year":"1975","unstructured":"De Giorgi, E., Franzoni, T.: Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 8, 842\u2013850 (1975)","journal-title":"Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur."},{"key":"9289_CR17","volume-title":"Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics","author":"LC Evans","year":"1992","unstructured":"Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992)"},{"key":"9289_CR18","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1512\/iumj.2010.59.4249","volume":"59","author":"I Fonseca","year":"2010","unstructured":"Fonseca, I., Kr\u00f6mer, S.: Multiple integrals under differential constraints: two-scale convergence and homogenization. Indiana Univ. Math. J. 59, 427\u2013458 (2010)","journal-title":"Indiana Univ. Math. J."},{"key":"9289_CR19","unstructured":"Fonseca, I., Leoni, G.: Modern Methods in the Calculus of Variations: $$L^p$$ L p Spaces. In: Springer Monographs in Mathematics. Springer, New York (2007)"},{"key":"9289_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00386367","volume":"123","author":"I Fonseca","year":"1993","unstructured":"Fonseca, I., M\u00fcller, S.: Relaxation of quasiconvex functionals in $$BV(\\Omega; \\mathbb{R}^{p})$$ B V ( \u03a9 \u037e R p ) for integrands $$f(x, u, \\nabla u)$$ f ( x , u , \u2207 u ) . Arch. Rat. Mech. Anal. 123, 1\u201349 (1993)","journal-title":"Arch. Rat. Mech. Anal."},{"key":"9289_CR21","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1137\/S0036141098339885","volume":"30","author":"I Fonseca","year":"1999","unstructured":"Fonseca, I., M\u00fcller, S.: $${\\cal A}$$ A -quasiconvexity, lower semicontinuity, and Young measures. SIAM J. Math. Anal. 30, 1355\u20131390 (1999). (electronic)","journal-title":"SIAM J. Math. Anal."},{"key":"9289_CR22","unstructured":"Kreisbeck, C., Rindler, F.: Thin-film limits of functionals on $${\\cal A}$$ A -free vector fields. Indiana Univ. Math. J., (to appear). arXiv:1105.3848"},{"issue":"1\u20132","key":"9289_CR23","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s00526-009-0250-5","volume":"37","author":"J Kristensen","year":"2010","unstructured":"Kristensen, J., Rindler, F.: Relaxation of signed integrals in BV. Calc. Var. Partial Differ. Equ. 37(1\u20132), 29\u201362 (2010)","journal-title":"Calc. Var. Partial Differ. Equ."},{"issue":"1","key":"9289_CR24","first-page":"33","volume":"2","author":"D Lukkassen","year":"2002","unstructured":"Lukkassen, D., Nguetseng, G., Wall, P.: Two-scale convergence. Int. J. Pure Appl. Math. 2(1), 33\u201381 (2002)","journal-title":"Int. J. Pure Appl. Math."},{"issue":"1","key":"9289_CR25","first-page":"69","volume":"8","author":"F Murat","year":"1981","unstructured":"Murat, F.: Compacit\u00e9 par compensation: condition n\u00e9cessaire et suffisante de continuit\u00e9 faible sous une hypothese de rang constante. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8(1), 69\u2013102 (1981)","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci."},{"key":"9289_CR26","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF00284506","volume":"99","author":"S M\u00fcller","year":"1987","unstructured":"M\u00fcller, S.: Homogenization of nonconvex integral functionals and cellular elastic materials. Arch. Rat. Mech. Anal. 99, 189\u2013212 (1987)","journal-title":"Arch. Rat. Mech. Anal."},{"key":"9289_CR27","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1137\/0520043","volume":"20","author":"G Nguetseng","year":"1989","unstructured":"Nguetseng, G.: A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20, 608\u2013623 (1989)","journal-title":"SIAM J. Math. Anal."},{"key":"9289_CR28","doi-asserted-by":"crossref","first-page":"537","DOI":"10.2307\/1971410","volume":"125","author":"D Preiss","year":"1987","unstructured":"Preiss, D.: Geometry of measures in $$\\mathbb{R}^{N}$$ R N : distributions, rectifiability and densities. Ann. Math. 125, 537\u2013643 (1987)","journal-title":"Ann. Math."},{"issue":"2","key":"9289_CR29","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1515\/acv.2011.008","volume":"5","author":"R Rindler","year":"2012","unstructured":"Rindler, R.: Lower semicontinuity and Young measures in BV without Alberti\u2019s rank-one theorem. Adv. Calc. Var. 5(2), 127\u2013159 (2012)","journal-title":"Adv. Calc. Var."},{"key":"9289_CR30","unstructured":"Tartar, L.: Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. IV (ed. R. Knops), Pitman. Res. Notes Math. 39, 136\u2013212 (1979)"}],"container-title":["Applied Mathematics & Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00245-015-9289-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00245-015-9289-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00245-015-9289-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T23:14:03Z","timestamp":1717715643000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00245-015-9289-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,3]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["9289"],"URL":"https:\/\/doi.org\/10.1007\/s00245-015-9289-1","relation":{},"ISSN":["0095-4616","1432-0606"],"issn-type":[{"value":"0095-4616","type":"print"},{"value":"1432-0606","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,3]]}}}