Research-Propagation of Smallness for Solutions of 2D Elliptic Equations

Research

PDE Seminar

Propagation of Smallness for Solutions of 2D Elliptic Equations

Speaker: Yuzhe Zhu(The University of Chicago)
Time: Jun 19, 2024, 10:30-11:30
Location: Room M616, College of Science Building

Abstract

We will discuss several quantitative results on propagation of smallness for solutions of two-dimensional elliptic equations. In particular, the gradient of harmonic functions on Hölder surfaces can be quantitatively estimated from sets of positive Hausdorff dimensions. We will also talk about their applications to spectral inequalities and controllability results for heat equations.