Averaging of singularly perturbed elliptic operators
The authors consider a family of operators of the form \[ L_{\epsilon}=\epsilon^{2\ell}\sum_{| \alpha | =| \beta | =m_ 1}(-1)^{m_ 1}D^{\alpha}(a_{\alpha \beta}(\epsilon^{-1}x)D^{\beta})+\sum_{| \alpha | =| \beta | =m}(-1)^ mD^{\alpha}(a_{\alpha \beta}(\epsilon^{- 1}x)D^{\beta}), \] where \(\ell =m_ 1-m>0\), \(\epsilon >0\) is a small parameter. They determine conditions for the coefficients \(\{a_{\alpha \beta}(x)\}\) such that the family \(L_{\epsilon}\) has a strong G-limit for \(\epsilon\) \(\to 0\).
scientific article; zbMATH DE number 3886361