论文标题
对于由复合材料产生的方程式解决方案解决方案的较高规律性
Higher regularity for solutions to equations arising from composite materials
论文作者
论文摘要
我们考虑以分段形式的抛物线系统$ c^{（s+δ）/2，s+δ} $系数和数据的系数和数据，其中包含有限数量的圆柱子域，具有$ c^{s+1+n $ s $ s $ s $ c n $ c^in $ C^{和$μ\ in（0,1] $。我们建立了分段$ c^{（s+1+μ'）/2，s+1+1+μ'} $估计了此类抛物线系统的弱解决方案，其中$μ'= \ min \ min \ big \ big \ big \ \ big \ {1/2，μ\ big \ big \ big \} $，以及估计的距离是独立的，彼此之间的距离是互动的。 （C）在Li和Vogelius中（Arch。Mech。Anal。153（2000），91--151）。
We consider parabolic systems in divergence form with piecewise $C^{(s+δ)/2,s+δ}$ coefficients and data in a bounded domain consisting of a finite number of cylindrical subdomains with interfacial boundaries in $C^{s+1+μ}$, where $s\in\mathbb N$, $δ\in (1/2,1)$, and $μ\in (0,1]$. We establish piecewise $C^{(s+1+μ')/2,s+1+μ'}$ estimates for weak solutions to such parabolic systems, where $μ'=\min\big\{1/2,μ\big\}$, and the estimates are independent of the distance between the interfaces. In the elliptic setting, our results answer an open problem (c) in Li and Vogelius (Arch. Rational Mech. Anal. 153 (2000), 91--151).
