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

Guido De Philippis, Luca Spolaor, Bozhidar Velichkov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)347-394
Number of pages48
JournalInventiones Mathematicae
Issue number2
StatePublished - Aug 2021

ASJC Scopus subject areas

  • General Mathematics


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