Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature

  • Andreas Gastel

    Universität Duisburg-Essen, Essen, Germany
  • Patrizio Neff

    Universität Duisburg-Essen, Essen, Germany
Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature cover

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Abstract

We consider the rigorously derived thin shell membrane -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation and the orthogonal microrotation tensor field . The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet-type energy term . We use Rivière’s regularity techniques of harmonic-map-type systems for our system which couples harmonic maps to with a linear equation for . The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.

Cite this article

Andreas Gastel, Patrizio Neff, Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/108