Large-scale Regularity of Nearly Incompressible Elasticity in Stochastic Homogenization

Shu Gu, Jinping Zhuge

Published 2020-04-30Version 1

In this paper, we systematically study the regularity theory of the linear system of nearly incompressible elasticity. In the setting of stochastic homogenization, we develop new techniques to establish the large-scale estimates of displacement and pressure, which are uniform in both the scale parameter and the incompressibility parameter. In particular, we obtain the boundary estimates in a new class of Lipschitz domains whose boundaries are smooth at large scales and bumpy at small scales.