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A homogenization result for a family of oscillating integral energies
is presented, where the fields are subjected to first order linear differential constraints depending on the space variable . The work is based on the theory of -quasiconvexity with variable coefficients and on two-scale convergence techniques, and generalizes the previously obtained results in the case in which the differential constraints are imposed by means of a linear first order differential operator with constant coefficients. The identification of the relaxed energy in the framework of -quasiconvexity with variable coefficients is also recovered as a corollary of the homogenization result.
Cite this article
Elisa Davoli, Irene Fonseca, Periodic homogenization of integral energies under space-dependent differential constraints. Port. Math. 73 (2016), no. 4 pp. 279–317