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

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.