Nonlocal Continuum Limits of p-Laplacian Problems on Graphs
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Sprache:Englisch
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Ja
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Ja
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Nein
Erscheinungsdatum
26.04.2023
Verlag
Cambridge University PressSeitenzahl
(Printausgabe)
Dateigröße
10595 KB
Sprache
Englisch
EAN
9781009327879
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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