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arXiv · 2604.23843

Fine structure of the two-phase Bernoulli free boundaries in 2D

Lorenzo Ferreri·Luca Spolaor·Bozhidar Velichkov
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Abstract

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.

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Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov. 2026-04-26. Fine structure of the two-phase Bernoulli free boundaries in 2D. https://arxiv.org/abs/2604.23843

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