论文标题
具有Dirichlet和非线性robin条件的非晶状穿孔域的操作员估计：奇怪的术语
Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term
论文作者
论文摘要
我们考虑具有精细穿孔的域中一般二阶线性方程的一般二阶线性方程的边界值问题。后者是由小腔制成的。空腔的形状及其分布都是任意的。腔的边界要么受到差异或非线性罗宾条件的约束。在穿孔上，施加了某些相当弱的条件，以确保在均质化下，我们在不构造的域中获得类似的问题，该域在方程式中具有额外的潜力，通常称为奇怪的术语。我们的主要结果表明，在$ W_2^1 $ - $ W_2^1 $ - 和$ L_2 $ -NORMS中的均匀问题的解决方案的融合均匀地均以$ L_2 $ - 等式中右侧的右侧。建立了收敛速率的估计值，并讨论了它们的顺序清晰度。
We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries of the cavities are subject either to a Dirichlet or a nonlinear Robin condition. On the perforation, certain rather weak conditions are imposed to ensure that under the homogenization we obtain a similar problem in a non-perforated domain with an additional potential in the equation usually called a strange term. 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. The estimates for the convergence rates are established and their order sharpness is discussed.
