Nodal Sets and Doubling Conditions in Elliptic Homogenization
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.