Wei Wang, Ting Zhang
Published 2022-10-12Version 1
In this paper, we consider the homogenization problem for generalized elliptic systems $$ \mathcal{L}_{\va}=-\operatorname{div}(A(x/\va)\nabla+V(x/\va))+B(x/\va)\nabla+c(x/\va)+\lambda I $$ with dimension two. Precisely, we will establish the $ W^{1,p} $ estimates, H\"{o}lder estimates, Lipschitz estimates and $ L^p $ convergence results for $ \mathcal{L}_{\va} $ with dimension two. The operator $ \mathcal{L}_{\va} $ has been studied by Qiang Xu with dimension $ d\geq 3 $ in \cite{Xu1,Xu2} and the case $ d=2 $ is remained unsolved. As a byproduct, we will construct the Green functions for $ \mathcal{L}_{\va} $ with $ d=2 $ and their convergence rates.
Uniform Regularity Estimates in Homogenization Theory of Elliptic Systems with Lower Order Terms on the Neumann Boundary Problem
Regularity theory and Green's function for elliptic equations with lower order terms in unbounded domains
Effect of lower order terms on the well-posedness of Majda-Biello systems
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