Let \(\Omega \) be an open set. We consider the supremal functional

applied to locally Lipschitz mappings \(u : \mathbb {R}^n \supseteq \Omega \longrightarrow \mathbb {R}^N\), where \(n,N\in \mathbb {N}\). This is the model functional of Calculus of Variations in \(L^\infty \). The area is developing rapidly, but the vectorial case of \(N\ge 2\) is still poorly understood. Due to the non-local nature of (1), usual minimisers are not truly optimal. The concept of so-called absolute minimisers is the primary contender in the direction of variational concepts. However, these cannot be obtained by direct minimisation and the question of their existence under prescribed boundary data is open when \(n,N\ge 2\). We present numerical experiments aimed at understanding the behaviour of minimisers through a new technique involving p-concentration measures.

令\（\ Omega \）为开放集。我们认为至上的功能

适用于本地Lipschitz映射\（u：\ mathbb {R} ^ n \ supseteq \ Omega \ longrightarrow \ mathbb {R} ^ N \），其中\（n，N \ in \ mathbb {N} \）。这是\（L ^ \ infty \）中的微积分计算的模型功能。该地区发展迅速，但对\（N \ ge 2 \）的矢量情况仍然知之甚少。由于（1）的非局部性质，通常的最小化并不是真正的最优。所谓绝对最小化器的概念是变分概念方向上的主要竞争者。但是，这些不能通过直接最小化来获得，并且在\（n，N \ ge 2 \）下在规定的边界数据下它们的存在问题是开放的。。我们目前的数值实验旨在通过涉及p浓度测量的新技术来理解最小化器的行为。