On the geometric properties of multi-operator two-phase elliptic measure
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918135780605952 |
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| author | Goering, Max Skorobogatova, Anna |
| author_facet | Goering, Max Skorobogatova, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometric properties of multi-operator two-phase elliptic measure Goering, Max Skorobogatova, Anna Analysis of PDEs 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. |
| title | On the geometric properties of multi-operator two-phase elliptic measure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.04189 |