In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. Subsequently, we present consistent monotone schemes to approximate infinity ground states and higher eigenfunctions on grids. We prove that our method converges (up to a subsequence) to a viscosity solution of the eigenvalue problem, and perform numerical experiments which investigate theoretical conjectures and compute eigenfunctions on a variety of different domains.

翻译：本文提出了与无穷Laplacian相关的高阶特征值问题的一种替代公式，为特征函数的数值逼近开辟了道路。我们通过严格分析证明了新公式与传统公式的等价性。随后，提出了一致的单调格式，用于在网格上逼近无穷基态与高阶特征函数。我们证明了该方法（按子序列收敛）收敛于特征值问题的粘性解，并通过数值实验探讨了理论猜想，同时在多种不同区域上计算了特征函数。