Regularity of Weak Solution of Variational Problems Modeling the Cosserat Micropolar Elasticity
Keyword(s):
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 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 $p\in [2, \frac{32}{15}]$.
2017 ◽
Vol 355
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pp. 359-362
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1985 ◽
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2003 ◽
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pp. 2735-2746
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1994 ◽
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2017 ◽
Vol 147
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pp. 449-503
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