In bounded convex domains, the regularity of a vector field u with its $\mathrm{div}\mathbf{u}$, $\mathrm{curl}\mathbf{u}$ in $L^r$ space and the tangential component or the normal component of u over the boundary in $L^r$ space, is established for $1<r<\infty$. As an application, we derive an $H^r(\mathrm{curl},\mathrm{\Omega })$ estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space $H^r(\mathrm{curl},\mathrm{\Omega })$ for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal.

中文翻译：

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关于凸域中麦克斯韦型系统的 Hr(curl,Ω) 估计

在有界凸域中，向量场u的正则性与其$\mathrm{div}\mathbf{你}$, $\mathrm{卷曲}\mathbf{你}$ 在 ${升}^r$空间和u在边界上的切向分量或法向分量${升}^r$ 空间，为 $1<r<\infty$. 作为一个应用程序，我们推导出一个$H^r(\mathrm{卷曲},\mathrm{\Omega })$估计在凸域中具有非均匀边界条件的麦克斯韦型系统的解。与空间中r的适定区域相反$H^r(\mathrm{卷曲},\mathrm{\Omega })$ 对于 Kar 和 Sini (2016) [16] 给出的 Lipschitz 域中的 Maxwell 类型系统，我们将适定区域扩展为最优。