论文标题
非晶状穿孔域的操作员估计：腔消失
Operator estimates for non-periodically perforated domains: disappearance of cavities
论文作者
论文摘要
我们考虑了穿孔域中一般二阶线性方程的一个边界值问题。穿孔是由小空腔制成的，腔之间的距离也很小。我们在腔的形状上施加了最小的自然几何条件，并且在其在域中的分布没有条件。在空腔的边界上，施加了非线性的罗宾条件。腔的大小和它们之间的最小距离应满足某种简单的条件，以确保在均匀化下消失，并且我们在非固定域中获得了类似的问题。我们的主要结果表明，在$ W_2^1 $ - $ W_2^1 $ - 和$ l_2 $ - norms中均匀的均质问题的解决方案的趋同均匀地均以$ l_2 $ - 右侧方程式中的右侧范围，并提供估算值的估计值。我们还讨论了这些估计的顺序清晰度。
We consider a boundary value problem for a general second order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions on the shapes of the cavities and no conditions on their distribution in the domain. On the boundaries of the cavities a nonlinear Robin condition is imposed. The sizes of the cavities and the minimal distance between them are supposed to satisfy a certain simple condition ensuring that under the homogenization the cavities disappear and we obtain a similar problem in a non-perforated domain. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in $W_2^1$- and $L_2$-norms uniformly in $L_2$-norm of the right hand side in the equation and provide the estimates for the convergence rates. We also discuss the order sharpness of these estimates.
