Regularity of Weak Solution of Variational Problems Modeling the Cosserat Micropolar Elasticity.

In this paper, we consider weak solutions of the Euler–Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling between the Poisson equation and the equation of |$p$| -harmonic maps (⁠|$2\le p\le 3$|⁠). We show that if a weak solution is stationary, then its singular set is discrete for |$2<p<3$| and has zero one-dimensional Hausdorff measure for |$p=2$|⁠. If, in addition, it is a stable-stationary weak solution, then it is regular everywhere when |$p\in [2, \frac{32}{15}]$|⁠. [ABSTRACT FROM AUTHOR]