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Extra info for A-quasiconvexity relaxation and homogenization
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Vitali, Homogenization of free–discontinuity problems, Arch. Rat. Mech. , 135 (1996), pp. 297–356.  G. Buttazzo, Semicontinuity, relaxation and integral representation problems in the Calculus of Variations, Pitman Res. Notes in Math. 207, Longman, Harlow, 1989.  B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989.  B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity for Nonlinear Functionals, Vol 922, Springer Lecture Notes in Mathematics, Springer-verlag, Berlin, 1982.