APDE seminar@BCAM: Quantitative characterizations of weights and parabolic boundary value problems

Abstract

Weights (non-negative locally integrable functions) satisfying a reverse H\"older condition are important in the study of harmonic measure and boundary value problems for elliptic and parabolic partial differential equations. In this talk, I will discuss a quantitative version of a Carleson measure characterization of reverse Hölder weights (originally found by Fefferman, Kenig and Pipher in the 90s) and its application to elliptic measure. In addition, I will explain extensions and modifications of the results needed in the analogous theory for parabolic measures. This is based on joint work with Simon Bortz and Moritz Egert.