@article{Yeh2024, 
author = {Li-Ming Yeh},
title = {Lipschitz estimate for elliptic equations with oscillatory coefficients},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {29135-29166},
keywords = {Lipschitz estimate, permeability, periodic size, Green's function, oscillatory coefficient},
url = {https://www.sciopen.com/article/10.3934/math.20241413},
doi = {10.3934/math.20241413},
abstract = {Regularity for elliptic equations with oscillatory coefficients was concerned. Problem domains were periodic and consisted of a connected region with normal permeability and a disconnected matrix block subset with high permeability. Coefficients of the elliptic equations depending on the permeability of the domains were highly oscillatory. Let  ϵ∈(0,1) be the periodic size of domain,  ϵμ∈(0,1) the size ratio of a matrix block to the whole domain, and  ω2∈(1,∞) the permeability ratio of the disconnected matrix block subset to the connected sub-region of the domains. This work presented Lipschitz estimate uniformly in  ϵ,μ,ω for the Green's functions and the solutions of the elliptic equations.}
}