无穷拉普拉斯特征值问题：重新表述与一种数值格式

一种用于无穷拉普拉斯的自适应有限元方法

An adaptive finite element method for the infinity Laplacian

本文提出一种用于无穷拉普拉斯方程的自适应有限元方法，通过后验分析和残差估计器驱动自适应算法，实现最优收敛性。

A non-local gradient based approach of infinity Laplacian with $Γ$-convergence

We propose an infinity Laplacian method to address the problem of interpolation on an unstructured point cloud. In doing so, we find the labeling function with the smallest infinity norm of its gradient. By introducing the non-local gradient, the continuous functional is approximated with a discrete form. The discrete problem is convex and can be solved efficiently with the split Bregman method. Experimental results indicate that our approach provides consistent interpolations and the labeling functions obtained are globally smooth, even in the case of extreme low sampling rate. More important…

Infinity-Laplacians on Scalar- and Vector-Valued Functions and Optimal Lipschitz Extensions on Graphs

Extending functions from boundary values plays an important role in various applications. In this thesis we consider discrete and continuous formulations of the problem based on $p$-Laplacians, in particular for $p=\infty$ and tight Lipschitz extensions. The thesis gives an overview of the existing theory and provides some novel results on the approximation of tight Lipschitz extensions for vector-valued functions.

分数拉普拉斯算子的弱奇异表达式

Weakly-singular formulation of the Fractional Laplacian operator

本文提出了一种分数拉普拉斯算子的弱奇异表达式，通过结合经典拉普拉斯算子和弱奇异积分算子，实现了高效准确的数值计算。

无穷拉普拉斯和p-拉普拉斯方程的有限差分方法

Finite difference methods for the Infinity Laplace and p-Laplace equations

针对无穷拉普拉斯和博弈论p-拉普拉斯方程，构建了收敛的离散格式和半隐式求解器，简化并推广了早期方法，证明了宽模板有限差分格式的解收敛到唯一粘性解，且半隐式求解器迭代次数与问题规模无关。

欧几里得首达渗流的比率收敛速度：对图无穷拉普拉斯算子的应用

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian

本文证明了在连通性阈值长度尺度上图无穷拉普拉斯方程的首个定量收敛速度，通过研究欧几里得首达渗流中距离函数的比率收敛性，并应用于Lipschitz学习。