Ke-Han Shi

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math.AP2026

A Nonlocal $p$ -Laplacian Interface Model with Sharp Interface

Kehan Shi, Zuoqiang Shi, Tangjun Wang

We propose an energy-based nonlocal $p$ -Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced t…

math.AP2026

Continuum limit of hypergraph $p$ -Laplacian equations on point clouds

Kehan Shi

This paper studies a class of $p$ -Laplacian equations on point clouds that arise from hypergraph learning in a semi-supervised setting. Under the assumption that the point clouds c…

math.AP2024

Continuum limit of $p$ -biharmonic equations on graphs

Kehan Shi, Martin Burger

This paper studies the $p$ -biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$ -Laplacian from the p…

A Nonlocal p-Laplacian Interface Model with Sharp Interface

Continuum limit of hypergraph p-Laplacian equations on point clouds

Continuum limit of p-biharmonic equations on graphs

A Nonlocal $p$ -Laplacian Interface Model with Sharp Interface

Continuum limit of hypergraph $p$ -Laplacian equations on point clouds

Continuum limit of $p$ -biharmonic equations on graphs