Fine structure of the two-phase Bernoulli free boundaries in 2D
Analysis of PDEs
2026-04-28 v1
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.
Keywords
Cite
@article{arxiv.2604.23843,
title = {Fine structure of the two-phase Bernoulli free boundaries in 2D},
author = {Lorenzo Ferreri and Luca Spolaor and Bozhidar Velichkov},
journal= {arXiv preprint arXiv:2604.23843},
year = {2026}
}