On the geometric properties of multi-operator two-phase elliptic measure

Abstract

We provide a structural characterization of a given boundary using two-phase elliptic measure in a multi-operator setting, extending to this novel setting results of Kenig, Preiss & Toro, Toro & Zhao and Azzam & Mourgoglou, including the validity of Oksendal's conjecture for two-sided NTA domains under the assumption of mutual absolute continuity of the elliptic measures. Our techniques rely on a reduction to a multi-operator two-phase free-boundary problem combined with an extension of the powerful tools introduced by Preiss in his Density Theorem.

Minor corrections done, and the main result now includes the validity of Oksendal's conjecture in this setting. 27 pages, comments welcome!