Preprint

Inserted: 4 sep 2025
Last Updated: 4 sep 2025

Year: 2025

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 a partial answer to Bishop's question regarding the validity of Oksendal's conjecture 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.

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