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arXiv · 2509.04189

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

Max Goering·Anna Skorobogatova
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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.

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Max Goering, Anna Skorobogatova. 2025-09-04. On the geometric properties of multi-operator two-phase elliptic measure. https://arxiv.org/abs/2509.04189

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