论文标题
具有$ C^{1，γ} $的复合材料的几何结果 - 边界
A geometric result for composite materials with $C^{1,γ}$-boundaries
论文作者
论文摘要
在本文中，我们获得了与椭圆形和抛物线部分微分方程相关的复合材料的几何结果。在古典论文中，Li and Vogelius（2000）以及Li和Nirenberg（2003）中，他们假设在任何规模上，并且在任何一点上都存在一个坐标系，使得复合材料的各个组件的边界本地在本地成为$ C^{1，γ} $ - 图。我们证明，如果复合材料的各个组件由$ c^{1，γ} $ - 边界组成，那么Li and Vogelius（2000）中的这种坐标系统以及Li and Li and Nirenberg（2003）存在，因此存在梯度界限和段落的梯度梯度连续性材料，以使其相关的Ellipt Ellipt ellipt eellipt systems与Systems相关。
In this paper, we obtain a geometric result for composite materials related to elliptic and parabolic partial differential equations. In the classical papers Li and Vogelius (2000), and Li and Nirenberg (2003), they assumed that for any scale and for any point there exists a coordinate system such that the boundaries of the individual components of a composite material locally become $C^{1,γ}$-graphs. We prove that if the individual components of a composite material are composed of $C^{1,γ}$-boundaries then such a coordinate system in Li and Vogelius (2000), and Li and Nirenberg (2003) exists, and therefore obtaining the gradient boundedness and the piecewise gradient Hölder continuity results for linear elliptic systems related to composite materials.
