G. De Philippis - M. Engelstein - L. Spolaor - B. Velichkov
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
Preprint
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Inserted: 28 jul 2021
Last Updated: 13 nov 2026
Year: 2021
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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