中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：申仲伟（肯塔基大学）

题  目：Nodal and Critical Sets of Solutions in Elliptic Homogenization

时  间：2023.05.30（星期二）10:30-11:30

地  点：S813

摘  要：In this talk I will describe my recent work, joint with Fanghua Lin, on the geometric properties of solutions of partial differential equations in the homogenization theory. We consider second-order elliptic equations with rapidly oscillating and periodic coefficients. We show that the (d-1)-dimensional Hausdorff measures of the nodal sets and the (d-2)-dimensional Hausdorff measures of the critical sets are bounded uniformly with respect to the period, provided that the doubling indices for the solutions are bounded. The proof uses the doubling inequality and the harmonic approximation successively. The key is to control accumulated errors by renormalization and rescaling.