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

We consider the rigorously derived thin shell membrane Γ -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation m ω⊂ R²→ R³ and the orthogonal microrotation tensor field R ω⊂ R²→ SO(3) . The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet-type energy term |DR|² . We use Rivière’s regularity techniques of harmonic-map-type systems for our system which couples harmonic maps to SO(3) with a linear equation for m . The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.