Journal Article

PUBDB-2026-01103

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Continuum Limit of $p$-Biharmonic Equations on Graphs

Shi, K. (Corresponding author)Extern* ; Burger, M.DESY*

2025
SIAM Philadelphia, Pa.

This record in other databases:  

Please use a persistent id in citations: doi:10.1137/23M161639X  doi:10.3204/PUBDB-2026-01103

Abstract: 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 perspective of hypergraphs. The asymptotic behavior of the solution is investigated for the random geometric graph when the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted 𝑝-biharmonic equation with homogeneous Neumann boundary conditions. The result relies on the uniform 𝐿𝑝 estimates for solutions and gradients of nonlocal and graph Poisson equations. The 𝐿∞ estimates of solutions are also obtained as a byproduct.

---

Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)

Experiment(s):

1. No specific instrument

---

Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

---