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arXiv · 1912.12975

Regularity of weak solution of variational problems modeling the Cosserat micropolar elasticity

Yimei Li·Changyou Wang
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Abstract

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 solutions is stationary, then its singular set is discrete for $2<p<3$ and has zero $1$-dimensional Hausdorff measure for $p=2$. If, in addition, it is a stable-stationary weak solution, then it is regular everywhere when $p\in [2, \frac{32}{15}]$.

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Yimei Li, Changyou Wang. 2019-12-30. Regularity of weak solution of variational problems modeling the Cosserat micropolar elasticity. https://arxiv.org/abs/1912.12975

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