Caleson Estimates on Solutions in Domains with Uniformly Rectifiable Boundaries

Explore elliptic operators and their associated measures in domains with uniformly rectifiable boundaries in this 28-minute lecture. Delve into the properties of domains Ω subset R^n with d-dimensional uniformly rectifiable boundaries, considering cases where d is less than n-1 and equal to n-1. Examine elliptic operators in the form L=-divAΔ with Dahlber-Kenig-Pipher coefficients. Learn about estimates on elliptic measures and their relationship to Hausdorff measures, as well as properties of Green functions associated with these operators. Cover key concepts such as uniform rectifiability, carousel measure condition, and the implications for elliptic measure and Green function behavior in these domains.