Minimizers of the multiphase vectorial Bernoulli functional exist, are locally Lipschitz, avoid triple points on the free boundary, and have C^{1,η} regularity near two-phase and branching points.
arXiv preprint arXiv:2107.12485 , year=
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On a Multiphase Vectorial Bernoulli Free Boundary Problem
Minimizers of the multiphase vectorial Bernoulli functional exist, are locally Lipschitz, avoid triple points on the free boundary, and have C^{1,η} regularity near two-phase and branching points.