{
  "id": "2308.00594",
  "version": "v1",
  "published": "2023-08-01T15:11:06.000Z",
  "updated": "2023-08-01T15:11:06.000Z",
  "title": "An operator-asymptotic approach to periodic homogenization applied to equations of linearized elasticity",
  "authors": [
    "Yi-Sheng Lim",
    "Josip Žubrinić"
  ],
  "comment": "48 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We explain an operator-asymptotic approach to homogenization for periodic composite media. This approach was developed by Cherednichenko and Vel\\v{c}i\\'c in [Cherednichenko and Vel\\v{c}i\\'c (2022) Sharp operator-norm asymptotics for thin elastic plates with rapidly oscillating periodic properties. J. London Math. Soc.] in the context of thin elastic plates, and here we demonstrate the approach under the simpler setting of equations of linearized elasticity. As a consequence, we obtain $L^2\\to L^2$, $L^2\\to H^1$, and higher order $L^2\\to L^2$ norm-resolvent estimates. The correctors for the $L^2\\to H^1$, and higher order $L^2\\to L^2$ results are constructed from boundary value problems that arise during the asymptotic procedure, and the first-order corrector is shown to coincide with classical formulae.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-01T15:11:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator-asymptotic approach",
      "linearized elasticity",
      "periodic homogenization",
      "thin elastic plates",
      "higher order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}