Modul: MAT675 PDE and Mathematical Physics

## Uniform rectifiability, harmonic measure and Carleson measure estimates for bounded harmonic functions

Dr. Mihalis Mourgoglou talk

Speaker invited by: Prof. Dr. Xavier Ros-Oton

**Date:** 04.04.19 **Time:** 14.00 - 15.00 **Room:** Y27H12

In this talk we will give an overview of the recent developments on free boundary problems for harmonic measure. In particular, we will discuss the connection between uniform rectifiability of the boundary of the domain with scale invariant PDE estimates for bounded harmonic functions as well as certain quantitative absolute continuity assumptions for harmonic measure with respect to the Hausdorff measure on the boundary.