We solve two variants of the Reifenberg problem (minimizing or not the free boundary) for all coefficient groups. We carry out the direct method of the calculus of variation and search a solution as a "weak limit" of a minimizing sequences. This strategy has been introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi and allowed them to solve the Reifenberg problem. We use an analogous strategy proved which has the advantage to take into account the free boundary. Moreover, we show that the Reifenberg class is closed under weak limits without restriction on the coefficient group.

中文翻译：

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（自由边界）Reifenberg Plateau 问题的解

我们为所有系数组解决 Reifenberg 问题的两个变体（最小化或不最小化自由边界）。我们执行变分法的直接方法并寻找一个解作为最小化序列的“弱极限”。De Lellis、De Philippis、De Rosa、Ghiraldin 和 Maggi 引入了这种策略，并允许他们解决 Reifenberg 问题。我们使用了一个类似的策略，证明它具有考虑自由边界的优势。此外，我们表明 Reifenberg 类在弱限制下是封闭的，而不受系数组的限制。