论文标题
关于具有局部周期性系数的椭圆差分运算符的分解近似值
On resolvent approximations of elliptic differential operators with locally periodic coefficients
论文作者
论文摘要
我们研究了渐近行为，因为小参数$ \ varepsilon $倾向于零，即均匀椭圆形的二阶差分差分算子的分解，其本地周期性系数取决于缓慢的可变$ x $，并且仅在快速可变的情况下具有固定性$ x/\ varepsilon $。我们在$ l^2 $ - 操作员融合的意义上为这些分解的操作员渐近学中的领先术语提供了构造，该构造与$ \ varepsilon^2 $剩余估计值。我们将第一个近似值的修改方法与移位的使用一起应用。
We study the asymptotic behaviour, as the small parameter $\varepsilon$ tends to zero, of the resolvents of uniformly elliptic second-order differential operators with locally periodic coefficients depending on the slow variable $x$ and the fast variable $x/\varepsilon$, with periodicity only in the fast variable. We provide a construction for the leading terms in the operator asymptotics of these resolvents in the sense of $L^2$-operator-norm convergence with order $\varepsilon^2$ remainder estimates. We apply the modified method of the first approximation with the usage of the shift.
