First-order homogenization

We provide a first-order homogenization result for quadratic functionals. In particular, we identify the scaling of the energy and the explicit form of the limiting functional in terms of the first-order correctors. The main novelty of the paper is the use of the dual correspondence between quadratic functionals and PDEs, combined with a refinement of the classical Riemann-Lebesgue Lemma.

💡 Research Summary

The paper investigates the first‑order homogenization of quadratic functionals defined on a periodically heterogeneous medium. The authors consider the family of energies
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