Homogenization of integral energies under periodically oscillating differential constraints

Abstract

A homogenization result for a family of integral energies $$\begin{aligned} u_{\varepsilon }\mapsto \int _\Omega f(u_{\varepsilon }(x))\,dx,\quad \varepsilon \rightarrow 0^+, \end{aligned}$$ is presented, where the fields \(u_{\varepsilon }\) are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of \(\mathscr {A}\)-quasiconvexity with variable coefficients and on two-scale convergence techniques.