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arXiv · 1805.09475

Nodal Sets and Doubling Conditions in Elliptic Homogenization

Fanghua Lin·Zhongwei Shen
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Abstract

This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators $\{ \mathcal{L}_\e\}$ in divergence form with rapidly oscillating and periodic coefficients. We show that the $(d-1)$-dimensional Hausdorff measures of the nodal sets of solutions to $\mathcal{L}_\e (u_\e)=0$ in a ball in $\R^d$ are bounded uniformly in $\e>0$. The proof relies on a uniform doubling condition and approximation of $u_\e$ by solutions of the homogenized equation.

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Fanghua Lin, Zhongwei Shen. 2018-05-24. Nodal Sets and Doubling Conditions in Elliptic Homogenization. https://arxiv.org/abs/1805.09475

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