Uniform Estimates of Resolvents in Homogenization Theory of Elliptic Systems
Wang, Wei · arXiv (Cornell University) · 2022
In this paper, we study the estimates of resolvents $ R(λ,\mathcal{L}_{\varepsilon})=(\mathcal{L}_{\varepsilon}-λI)^{-1} $, where $$ \mathcal{L}_{\varepsilon}=-\operatorname{div}(A(x/\varepsilon) abla) $$ is a family of second elliptic operators with symmetric, periodic and oscillating coefficients defined on a bounded domain $ Ω$ with $ \varepsilon>0 $. For $ 1