Fine structure of the two-phase Bernoulli free boundaries in 2D
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911623631863808 |
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| author | Ferreri, Lorenzo Spolaor, Luca Velichkov, Bozhidar |
| author_facet | Ferreri, Lorenzo Spolaor, Luca Velichkov, Bozhidar |
| contents | We prove that the branching set of a solution to a two-dimensional two-phase Bernoulli problem with constant coefficients is locally finite. We do this via a Weierstrass representation formula, which allows to transform the problem into a new geometric two-phase problem for capillary minimal surfaces. We also apply this method to the obstacle problem establishing a connection between the directional derivatives of solutions to the obstacle problem and the linear thin two-membrane problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23843 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fine structure of the two-phase Bernoulli free boundaries in 2D Ferreri, Lorenzo Spolaor, Luca Velichkov, Bozhidar Analysis of PDEs We prove that the branching set of a solution to a two-dimensional two-phase Bernoulli problem with constant coefficients is locally finite. We do this via a Weierstrass representation formula, which allows to transform the problem into a new geometric two-phase problem for capillary minimal surfaces. We also apply this method to the obstacle problem establishing a connection between the directional derivatives of solutions to the obstacle problem and the linear thin two-membrane problem. |
| title | Fine structure of the two-phase Bernoulli free boundaries in 2D |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.23843 |