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

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