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.
- ISBN13 9781009327855
- Publish Date 11 May 2023 (first published 13 April 2023)
- Publish Status Active
- Publish Country GB
- Imprint Cambridge University Press
- Format Paperback (US Trade)
- Pages 75
- Language English