rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Two-scale tools for homogenization and dimension reduction of perforated thin layers
    sub title: extensions, Korn-inequalities, and compactness of scale-dependent sets in Sobolev spaces
  name:
    name part: Gahn, Markus
    role:
      role term: creator
    role:
      role term: VerfasserIn
    role:
      role term: aut
  name:
    name part: Jäger, Willi
    name part: 1940-
    role:
      role term: VerfasserIn
    role:
      role term: aut
  name:
    name part: Neuss-Radu, Maria
    role:
      role term: VerfasserIn
    role:
      role term: aut
  type of resource: text
  origin info:
    place:
      place term: xx
    date issued: 2026
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: Illustrationen
    extent: 34
  abstract: In this investigation, we develop basic methods for the multi-scale analysis of problems in thin porous layers. More precisely, we provide tools for the homogenization of “tangentially” periodic structures, and dimensional reduction letting the layer thickness tend to zero prop ortional to the scale parameter ϵ. A crucial point is the identification of scale limits of sequences vϵ characterized by uniform a priori estimates with respect to ϵ, arising as solutions of differential equations, like Navier-Stokes system, linear elasticity, or fluid-structure interaction problems, in media with thin layers. Often in such problems, in a first step, the symmetric gradients can be controlled, and Korn’s inequality in porous layers is required to estimate the gradients. We construct controllable pore-filling extensions and use them for the proof of the required Korn-inequalities in Lp-spaces. These results are the basis for the derivation of compactness results with respect to two-scale convergence and the characterization of the scale limits. To illustrate the range of application of the developed multi-scale methods, a semi-linear elastic wave equation in a thin periodically perforated layer with an inhomogeneous Neumann boundary condition on the surface of the elastic substructure is treated and a homogenized, reduced system is derived.
  note: Markus Gahn, Willi Jäger and Maria Neuss-Radu
  note: Gesehen am 10.04.2026
  classification: 27
  related item:
    title info:
      title: Asymptotic analysis
    name:
      name part: Two-scale tools for homogenization and dimension reduction of perforated thin layers extensions, Korn-inequalities, and compactness of scale-dependent sets in Sobolev spaces
    origin info:
      publisher: London : Sage, 1988
    physical description:
      extent: Online-Ressource
    identifier: 1875-8576
    identifier: (DE-627)320506681
    identifier: (DE-600)2012917-8
    identifier: (DE-576)094085706
    part:
      text: (2026), Seite 1-34
  related item:
    name:
      name part: Two-scale tools for homogenization and dimension reduction of perforated thin layers extensions, Korn-inequalities, and compactness of scale-dependent sets in Sobolev spaces
    part:
      text: year:2026
    part:
      text: pages:1-34
    part:
      text: extent:34
  identifier: https://doi.org/10.1177/09217134251406776
  identifier: https://journals.sagepub.com/doi/10.1177/09217134251406776
  record info:
    record content source: DE-627
    record creation date: 260410
    record change date: 20260410111656.0
    record identifier: 1968309527
    language of cataloging:
      language term: ger