Calculus of Variations and Geometric Measure Theory

G. De Philippis - M. Engelstein - L. Spolaor - B. Velichkov

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

created by velichkov on 28 Jul 2021
modified on 29 Jul 2021



Inserted: 28 jul 2021
Last Updated: 29 jul 2021

Year: 2021

ArXiv: 2107.12485 PDF


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.