## Publication 126

*Periodic Homogenization Of Integral Energies Under Space-Dependent Differential Constraints*

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##### Abstract:

A homogenization result for a family of oscillating integral energies $$ u_{\varepsilon} \rightarrow \int_{\Omega} f(x, \frac{x}{\varepsilon}, u_{\varepsilon}(x))dx, \ \ \ \varepsilon \rightarrow 0^+$$ is presented, where the fields $u_{\varepsilon}$ are subjected to first order linear differential constraints depending on the space variable $x$. The work is based on the theory of ${\cal A}$-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 ${\cal A}$-quasiconvexity with variable coefficients is also recovered as a corollary of the homogenization result.##### Get the paper in its entirety

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