Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition

• Published in: Geometric and functional analysis Vol. 31; no. 2; pp. 325 - 401
• Main Authors: Hofmann, Steve, Martell, José María, Mayboroda, Svitlana, Toro, Tatiana, Zhao, Zihui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2021; Springer Nature B.V
• Subjects: Analysis; Continuity; Domains; Euclidean geometry; Euclidean space; Mathematics; Mathematics and Statistics; Operators (mathematics); Rectifiability; Elliptic measure; 31B35; Uniform domain; 35J25; 42B37; class; Exterior corkscrew

The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic measure with respect to the surface measure and uniform rectif...