Analysis and PDE Seminar— Nodal Sets and Doubling Conditions in Elliptic Homogenization
主 题: Analysis and PDE Seminar— Nodal Sets and Doubling Conditions in Elliptic Homogenization
报告人: Zhongwei Shen (University of Kentucky)
时 间: 2018-05-25 10:30-11:30
地 点: Room 1303, Sciences Building No. 1
Abstract: This talk is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators in divergence form with rapidly oscillating periodic coefficients. We show that the (d-1)-dimensional Hausdorff measure of the nodal sets of solutions in a ball is uniformly bounded with respect to the inhomogeneity scale. The proof relies on a uniform doubling condition and approximation by solutions of the homogenized equation. This is a joint work with Fanghua Lin.
