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We consider the rigorously derived thin shell membrane $\Gamma$-limit of athree-dimensional isotropic geometrically nonlinear Cosserat micropolar modeland deduce full interior regularity of both the midsurface deformation$m:\omega\subset{\mathbb R}^2\to{\mathbb R}^3$ and the orthogonal microrotationtensor field $R:\omega\subset{\mathbb R}^2\to SO(3)$. The only furtherstructural assumption is that the curvature energy depends solely on theuni-constant isotropic Dirichlet type energy term $|DR|^2$. We use Rivi\`ere'sregularity techniques of harmonic map type systems for our system which couplesharmonic maps to $SO(3)$ with a linear equation for $m$. The additionalcoupling term in the harmonic map equation is of critical integrability and canonly be handled because of its special structure.

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