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：本文提出了一种与无穷拉普拉斯算子相关的高阶特征值问题的替代性表述，该表述为特征函数的数值逼近开辟了途径。通过严格分析证明新表述与传统表述的等价性。随后，我们提出了一致单调格式，用于在网格上逼近无穷基态及高阶特征函数。证明了该方法（在子列意义下）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，在多种不同域上计算了特征函数。