Calculus of Variations and Geometric Measure Theory
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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 on 17 Dec 2020



Inserted: 4 nov 2019
Last Updated: 17 dec 2020

Year: 2019


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.


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