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arXiv · 1912.06720

Propagation of smallness in elliptic periodic homogenization

Carlos Kenig·Jiuyi Zhu
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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 $\mathcal{L}_\epsilon$ 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.

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Carlos Kenig, Jiuyi Zhu. 2019-12-13. Propagation of smallness in elliptic periodic homogenization. https://arxiv.org/abs/1912.06720

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