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

2025/09/04 by Max Goering, Anna Skorobogatova, Goering, Max +1
#math.AP

paper · pdf · doi:10.48550/arxiv.2509.04189

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.

Related

• On a two-phase problem for harmonic measure in general domains
• Elliptic theory in domains with boundaries of mixed dimension
• Elliptic and parabolic overdetermined problems in multi-phase settings
• A new elliptic measure on lower dimensional sets
• Two- and Multi-phase Quadrature Surfaces