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Nonlocal Continuum Limits of p-Laplacian Problems on Graphs (Elements in - Picture 2 of 2

Elements in Non-Local Data Interactions: Foundations and Applications Ser.: Nonlocal Continuum Limits of P-Laplacian Problems on Graphs by Yosra Hafiene, Abderrahim Elmoataz, Jalal Fadili and Imad El Bouchairi (2023, Trade Paperback)

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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.