论文标题
关于动态线性松弛微态模型中局部较高规律性的注释
A note on local higher regularity in the dynamic linear relaxed micromorphic model
论文作者
论文摘要
我们考虑了线性宽松的微态模型的动态初始有限值问题的规律性问题。该广义连续体模型将带动型的波型方程与微渗透的广义Maxwell-type波方程相结合。自然的解决方案是在$ {\ rm h}^1 $中的$ {\ u $和$ {\ rm h}（{\ rm curl}）$的$ {\ rm h} $。使用差异商的能量估计，我们提高了这种规律性。我们显示$ {\ rm h}^1 _ {\ rm loc} $ - 置换字段的规律性，$ {\ rm h}^1 _ {\ rm lok lok} $ - 微持续量张量$ p $的规律性，以及该$ {\ rm curl} uduff udgul，p $ $ - 光滑的。
We consider the regularity question of solutions for the dynamic initial-boundary value problem for the linear relaxed micromorphic model. This generalized continuum model couples a wave-type equation for the displacement with a generalized Maxwell-type wave equation for the micro-distortion. Naturally solutions are found in ${\rm H}^1$ for the displacement $u$ and ${\rm H}({\rm Curl})$ for the microdistortion $P$. Using energy estimates for difference quotients, we improve this regularity. We show ${\rm H}^1_{\rm loc}$-regularity for the displacement field, ${\rm H}^1_{\rm loc}$-regularity for the micro-distortion tensor $P$ and that ${\rm Curl}\,P$ is ${\rm H}^1$-regular if the data is sufficiently smooth.
