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 microdistortion. Naturally, solutions are found in H¹ for the displacement u and H(Curl) for the microdistortion P. Using energy estimates for difference quotients, we improve this regularity. We show ${\mathrm{H}}_{\text{loc}}^1$–regularity for the displacement field, ${\mathrm{H}}_{\text{loc}}^1$–regularity for the microdistortion tensor P and that $\text{Curl}P$ is H¹–regular if the data are sufficiently smooth.

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关于动态线性松弛微晶模型中局部较高正则性的注记

我们考虑线性松弛微晶模型的动态初边界值问题的解的规律性问题。该广义连续介质模型将位移的波型方程与微畸变的广义麦克斯韦型波动方程耦合。自然地，可以在 H ¹中找到位移u 的解和 H(Curl) 中微畸变P 的解。使用差商的能量估计，我们改进了这种规律性。我们展示${\mathrm{H}}_{\text{位置}}^1$– 位移场的规则性， ${\mathrm{H}}_{\text{位置}}^1$–微失真张量P 的正则性和$\text{卷曲}磷$如果数据足够平滑，则为 H ¹ -正则。