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arXiv · 2107.12485

Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries

Guido De Philippis·Max Engelstein·Luca Spolaor·Bozhidar Velichkov
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Abstract

We prove that for minimizers of the vectorial Alt-Caffarelli functional the two-phase singular set of the free boundary is rectifiable and the blow-up is unique almost everywhere on it. While the first conclusion is an application of the recent techniques developed by Naber and Valtorta, the uniqueness part follows from the rectifiability and a new application of the Alt-Caffarelli-Friedman monotonicity formula.

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Guido De Philippis, Max Engelstein, Luca Spolaor, Bozhidar Velichkov. 2021-07-26. Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries. https://arxiv.org/abs/2107.12485

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