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

Guido De Philippis; Luca Spolaor; Bozhidar Velichkov

doi:10.1007/s00222-021-01031-7

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

Guido De Philippis, Luca Spolaor, Bozhidar Velichkov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	347-394
Number of pages	48
Journal	Inventiones Mathematicae
Volume	225
Issue number	2
DOIs	https://doi.org/10.1007/s00222-021-01031-7
State	Published - Aug 2021

ASJC Scopus subject areas

General Mathematics

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10.1007/s00222-021-01031-7

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abstract = "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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AB - 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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Regularity of the free boundary for the two-phase Bernoulli problem

Abstract

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