We propose a monotone and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized infinity Laplacian, which could be related to the family of the so-called two-scale methods. We show that this method is convergent and prove rates of convergence. These rates depend not only on the regularity of the solution, but also on whether or not the right-hand side vanishes. Some extensions to this approach, like obstacle problems and symmetric Finsler norms, are also considered.

中文翻译：

---

归一化无穷拉普拉斯算子的两尺度方法：收敛率

我们提出了一种单调且一致的数值方案来近似归一化无穷大拉普拉斯的狄利克雷问题，这可能与所谓的双尺度方法系列有关。我们证明了该方法是收敛的并证明了收敛速度。这些比率不仅取决于解的规律性，还取决于右侧是否消失。还考虑了这种方法的一些扩展，例如障碍问题和对称芬斯勒范数。