论文标题
运算符估计具有差异和非线性罗宾条件的非晶状穿孔域：消失极限
Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit
论文作者
论文摘要
我们考虑在精细穿孔域中的一般二阶线性椭圆方程。空腔的形状及其在域中的分布是任意的和非周期性的。它们应该满足最小的自然几何条件。在空腔的边界上，我们施加了Dirichlet或非线性罗宾条件。每个腔的边界条件类型的选择是任意的。然后，我们假设在某些空腔中，非线性罗宾条件在某些意义上是标志性的。如果这种空腔和具有差异条件的空腔分布在域中，并且腔的特征大小以及腔之间的最小距离满足了某些简单条件，我们表明，由于穿孔变得更细，对我们问题的解决方案往往为零。我们的主要结果是$ l_2 $ - 和$ W_2^1 $ - norms的订单尖锐估计值 - 右侧右侧的$ L_2 $ norms的解决方案统一。
We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric conditions. On the boundaries of the cavities we impose either the Dirichlet or a nonlinear Robin condition; the choice of the type of the boundary condition for each cavity is arbitrary. Then we suppose that for some cavities the nonlinear Robin condition is sign-definite in certain sense. Provided such cavities and ones with the Dirichlet condition are distributed rather densely in the domain and the characteristic sizes of the cavities and the minimal distances between the cavities satisfy certain simple condition, we show that a solution to our problem tends to zero as the perforation becomes finer. Our main result are order sharp estimates for the $L_2$- and $W_2^1$-norms of the solution uniform in the $L_2$-norm of the right hand side in the equation.
