In this paper we study stationary graphs for functionals of geometric nature defined on currents or varifolds. The point of view we adopt is the one of differential inclusions, introduced in this context in the recent papers (De Lellis et al. in Geometric measure theory and differential inclusions, 2019. arXiv:1910.00335; Tione in Minimal graphs and differential inclusions. Commun Part Differ Equ 7:1–33, 2021). In particular, given a polyconvex integrand f, we define a set of matrices \(C_f\) that allows us to rewrite the stationarity condition for a graph with multiplicity as a differential inclusion. Then we prove that if f is assumed to be non-negative, then in \(C_f\) there is no \(T'_N\) configuration, thus recovering the main result of De Lellis et al. (Geometric measure theory and differential inclusions, 2019. arXiv:1910.00335) as a corollary. Finally, we show that if the hypothesis of non-negativity is dropped, one can not only find \(T'_N\) configurations in \(C_f\), but it is also possible to construct via convex integration a very degenerate stationary point with multiplicity.

在本文中，我们研究了定义在电流或变数上的几何性质泛函的平稳图。我们采用的观点是微分包含的观点之一，在最近的论文（De Lellis 等人，在几何测度理论和微分包含，2019 年。arXiv:1910.00335 中；Tione 在最小图形和微分包含中。Commun部分不同 Equ 7:1–33, 2021)。特别是，给定一个多凸被积函数f，我们定义了一组矩阵\(C_f\)，它允许我们将具有多重性的图的平稳性条件重写为微分包含。然后，我们证明了如果˚F被假定为不可否定的，那么在\（C_F \）没有\（T'_N \）配置，从而恢复了 De Lellis 等人的主要结果。（几何测度理论和微分包含，2019 年。arXiv:1910.00335）作为推论。最后，我们表明，如果非负的假说被丢弃，一个不仅可以找到\（T'_N \）配置在\（C_F \） ，但它也可以通过凸集成了非常退化驻点建设具有多样性。