Nodal Sets and Doubling Conditions in Elliptic Homogenization

作     者：Fanghua Lin Zhongwei Shen 

作者机构：Courant Institute of Mathematical Sciences Department of Mathematics University of Kentucky 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第6期

页      面：815-831页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by NSF(Grant No.DMS-1501000) supported in part by NSF(Grant No.DMS-1600520) 

主　　题：Nodal sets homogenization doubling condition 

摘      要：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 {L_ε} 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 L_ε(u_ε) = 0 in a ball in Rdare bounded uniformly in ε 0. The proof relies on a uniform doubling condition and approximation of u_ε by solutions of the homogenized equation.