2023/08/01 by Yi-Sheng Lim, Lim, Yi-Sheng, Josip Žubrinić +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Electromagnetic Scattering and Analysis #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2308.00594
openalex publication_date 2023/08/01 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
We present an operator-asymptotic approach to the problem of homogenization of periodic composite media in the setting of three-dimensional linearized elasticity. This is based on a uniform approximation with respect to the inverse wavelength |χ| for the solution to the resolvent problem when written as a superposition of elementary plane waves with wave vector (``quasimomentum") χ. We develop an asymptotic procedure in powers of |χ|, combined with a new uniform version of the classical Korn inequality. As a consequence, we obtain L2→ L2, L2→ H1, and higher-order L2→ L2 norm-resolvent estimates in ℝ3. The L2 → H1 and higher-order L2 → L2 correctors emerge naturally from the asymptotic procedure, and the former is shown to coincide with the classical formulae.