First-order homogenization

2025/05/24 by Cristoferi, Riccardo, D'Elia, Lorenza
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.18848

Abstract

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.

Citations

• Homogenization of supremal functionals in the vectorial case (via L^p-approximation)
• Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions
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• Homogenization and phase separation with space dependent wells -- The subcritical case
• Homogenization of discrete thin structures
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• Boundary Layers in Periodic Homogenization of Neumann Problems
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• Homogenization of layered materials with rigid components in single-slip finite crystal plasticity
• Continuity and Discontinuity of the Boundary Layer Tail
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• Asymptotic expansions by Γ-convergence

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