论文标题
在各向异性的恒定定理上通过差分包含
On the constancy theorem for anisotropic energies through differential inclusions
论文作者
论文摘要
在本文中，我们研究了在电流或varifolds上定义的几何性质功能的固定图。我们采用的观点是在最近的论文中引入的差异包裹物之一[de Lellis，de Philippis，Kirchheim，Tione，Tione，2019年]。特别是，给定一个polyconvex Integrand $ f $，我们定义了一组矩阵$ C_F $，该矩阵$ c_f $允许我们重写以差分包含为差分的图形的平稳条件。然后，我们证明，如果假定$ f $是非负的，则在$ c_f $中没有$ t'_n $配置，从而恢复了[de Lellis，de Philippis，Kirchheim，Tione，Tione，2019]的主要结果。最后，我们表明，如果删除了非阴性的假设，那么人们不仅可以在$ C_F $中找到$ t'_n $配置，而且还可以通过凸集成构建具有多重变性的静态固定点。
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 paper [De Lellis, De Philippis, Kirchheim, Tione, 2019]. 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, De Philippis, Kirchheim, Tione, 2019] 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.
