Calculus of Variations and Geometric Measure Theory

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

Regularity of the free boundary for the two-phase Bernoulli problem

created by velichkov on 04 Nov 2019
modified by dephilipp on 05 Jun 2023


Published Paper

Inserted: 4 nov 2019
Last Updated: 5 jun 2023

Journal: Inventiones mathematicae
Year: 2021

ArXiv: 1911.02165 PDF


We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.