Nodal Sets and Doubling Conditions in Elliptic Homogenization
Nodal Sets and Doubling Conditions in Elliptic Homogenization
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椭圆均匀化中的节点集和加倍条件
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Zhongwei Shen
中科院分区：
文献类型：
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作者：
F. Lin;Zhongwei Shen
本文研究椭圆齐次化方程节点解集的一致测度估计。考虑一类具有快速振荡和周期系数的二阶椭圆算子{Lε}.我们证明了Lε（uε）= 0在球中的解的节点集的（d-1）维Hausdorff测度在ε > 0中是一致有界的.证明依赖于一致的加倍条件和用齐次方程的解近似uε。
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 {Lε} 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 Lε(uε) = 0 in a ball in ℝd are bounded uniformly in ε > 0. The proof relies on a uniform doubling condition and approximation of uε by solutions of the homogenized equation.