Uniform Lipschitz Estimates in Bumpy Half-Spaces

Abstract

This paper is devoted to the proof of uniform Hölder and Lipschitz estimates close to oscillating boundaries, for divergence form elliptic systems with periodically oscillating coefficients. Our main point is that no structure is assumed on the oscillations of the boundary. In particular, those are neither periodic, nor quasiperiodic, nor stationary ergodic. We investigate the consequences of our estimates on the large scales of Green and Poisson kernels. Our work opens the door to the use of potential theoretic methods in problems concerned with oscillating boundaries, which is an area of active research.

54 pages

References in corpus (3)

• The Green function estimates for strongly elliptic systems of second order
• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• The Navier wall law at a boundary with random roughness

Cited by in corpus (4)

• Uniform Boundary Estimates in Homogenization of Higher Order Elliptic Systems
• Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
• Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations
• $L^2$-estimates for singular oscillatory integral operators