Abstract We consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein, and Toro. Our proofs provide a different method based on a non-infinitesimal notion of viscosity solutions that we introduced.

中文翻译：

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一相自由边界问题的几乎最小化

摘要 我们考虑了单相能量泛函的几乎极小值，并证明了它们的最优 Lipschitz 正则性和自由边界的部分正则性。这些结果最近由 David 和 Toro 以及 David、Engelstein 和 Toro 获得。我们的证明提供了一种基于我们引入的粘度解的非无穷小概念的不同方法。