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Series:   Elements in Non-local Data Interactions: Foundations and Applications

Nonlocal Continuum Limits of p-Laplacian Problems on Graphs

Published online by Cambridge University Press:  13 April 2023

Imad El Bouchairi ,
Jalal Fadili ,
Yosra Hafiene  and
Abderrahim Elmoataz
Imad El Bouchairi
Affiliation:
University of Caen Normandy
Jalal Fadili
Affiliation:
ENSICAEN
Yosra Hafiene
Affiliation:
ENSEEIHT
Abderrahim Elmoataz
Affiliation:
University of Caen Normandy

Summary

In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.
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Keywords

nonlocal p-Laplacianevolution problemvariational problemDirichlet problemnumerical approximationsrates of the convergencegraphonssparse graphs
Type
Element
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Series: Elements in Non-local Data Interactions: Foundations and Applications
Online ISBN: 9781009327862
Publisher: Cambridge University Press
Print publication: 11 May 2023

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