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.

中文翻译：

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两阶段伯努利问题的自由边界的规则性

我们证明了两相贝努利问题的极小值的自由边界的正则定理，从而完成了80年代由Alt，Caffarelli和Friedman开始的分析。结果，对于狄利克雷拉普拉斯算子的本征值，我们还显示了多相频谱优化问题的极小值的正则性。