Regularity theory of elliptic systems in $\epsilon$-scale flat domains

Abstract

We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called $\epsilon$-scale flatness condition, which could be arbitrarily rough below $\epsilon$-scale. This particularly generalizes Kenig and Prange's work in [32] and [33] by a quantitative approach.

arXiv comment28 pages, 1 figure, revised version

References in corpus (6)

• Quantitative stochastic homogenization and regularity theory of parabolic equations
• Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity
• Uniform Lipschitz Estimates in Bumpy Half-Spaces
• Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface
• Uniform boundary regularity in almost-periodic homogenization
• Weighted $L^2$ Estimates for Elliptic Homogenization in Lipschitz Domains