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.

Regularity of the free boundary for the two-phase Bernoulli problem / De Philippis, G.; Spolaor, L.; Velichkov, B.. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 225:2(2021), pp. 347-394. [10.1007/s00222-021-01031-7]

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

De Philippis G.;
2021-01-01

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.
2021
225
2
347
394
https://doi.org/10.1007/s00222-021-01031-7
https://arxiv.org/abs/1911.02165
De Philippis, G.; Spolaor, L.; Velichkov, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135474
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