Journal Article

PUBDB-2026-02062

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The Graph \(\boldsymbol{\infty }\)-Laplacian Eigenvalue Problem

Deidda, P. (Corresponding author) ; Burger, M.DESY* ; Putti, M. ; Tudisco, F.

2026
SIAM Philadelphia, Pa.

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Please use a persistent id in citations: doi:10.1137/24M1705342  doi:10.3204/PUBDB-2026-02062

Report No.: arXiv:2410.19666

Abstract: We analyze various formulations of the ∞-Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. First, we investigate the graph ∞-eigenpairs arising as limits of 𝑝-Laplacian eigenpairs, extending key results from the continuous setting to the discrete domain. We prove that every limit of 𝑝-Laplacian eigenpair, for 𝑝 going to ∞, satisfies a limit eigenvalue equation and establishes that the corresponding eigenvalue can be bounded from below by the packing radius of the graph, indexed by the number of nodal domains induced by the eigenfunction. Additionally, we show that the limits, for 𝑝 going to ∞, of the variational 𝑝-Laplacian eigenvalues are bounded from both above and below by the packing radii, achieving equality for the smallest two variational eigenvalues and corresponding packing radii of the graph. In the second part of the paper, we introduce generalized ∞-Laplacian eigenpairs as generalized critical points and values of the ∞-Rayleigh quotient. We prove that the generalized variational ∞-eigenvalues equal the limit of the 𝑝-Laplacian variational eigenvalues and so satisfy the same upper bounds in terms of packing radii. Finally, we establish that any solution to the limit eigenvalue equation is also a generalized eigenpair, while any generalized eigenpair satisfies the limit eigenvalue equation on a suitable subgraph.

Note: DFG support via the SFB TRR 154, Subproject C06.

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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

Appears in the scientific report 2026

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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

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