Propagation of smallness in elliptic periodic homogenization
Document Type
Article
Publication Date
1-1-2021
Abstract
The paper is mainly concerned with an approximate three-ball inequality for solutions in elliptic periodic homogenization. We consider a family of second order operators \scrL \epsilon in divergence form with rapidly oscillating and periodic coefficients. It is the first time such an approximate three-ball inequality for homogenization theory is obtained. It implies an approximate quantitative propagation of smallness. The proof relies on a representation of the solution by the Poisson kernel and the Lagrange interpolation technique. Another full propagation of smallness result is also shown.
Publication Source (Journal or Book title)
SIAM Journal on Mathematical Analysis
First Page
111
Last Page
132
Recommended Citation
Kenig, C., & Zhu, J. (2021). Propagation of smallness in elliptic periodic homogenization. SIAM Journal on Mathematical Analysis, 53 (1), 111-132. https://doi.org/10.1137/20M1312770