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This work deals with the homogenization of functionals with linear growth inthe context of $\mathcal{A}$-quasiconvexity. A representation theorem isproved, where the new integrand function is obtained by solving a cell problemwhere the coupling between homogenization and the $\mathcal{A}$-free conditionplays a crucial role. This result extends some previous work to the linearcase, thus allowing for concentration effects.

Homogenization of functional with linear growth in the context of $\mathcal{A}$-quasiconvexity