论文标题
无限拉普拉斯特征值问题：重新制定和数值方案
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
论文作者
论文摘要
在这项工作中，我们提出了与Infinity Laplacian相关的较高特征值问题的替代公式，该问题为特征函数的数值近似开辟了大门。进行了严格的分析，以显示新表述与传统表述的等效性。随后，我们呈现一致的单调方案，以近似于无限地面状态和网格上较高的本征函数。我们证明我们的方法将特征值问题的粘度解决方案收敛（直至子序列），并执行数值实验，这些实验研究了理论猜想并在各种不同领域上进行了特征函数。
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.
