{"date_published":"2024-12-20T00:00:00Z","type":"journal_article","_id":"18706","oa_version":"Published Version","author":[{"last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo"},{"id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo","last_name":"Quattrocchi","first_name":"Filippo","orcid":"0009-0000-9773-1931"}],"OA_place":"publisher","page":"1-29","date_created":"2024-12-23T11:03:59Z","doi":"10.1017/s0956792524000810","oa":1,"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1469-4425"],"issn":["0956-7925"]},"article_processing_charge":"Yes","DOAJ_listed":"1","scopus_import":"1","year":"2024","month":"12","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"date_updated":"2025-01-02T10:43:10Z","quality_controlled":"1","title":"Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs","article_type":"original","publication":"European Journal of Applied Mathematics","publisher":"Cambridge University Press","citation":{"ieee":"L. Portinale and F. Quattrocchi, “Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs,” <i>European Journal of Applied Mathematics</i>. Cambridge University Press, pp. 1–29, 2024.","mla":"Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits of Optimal Transport with Linear Growth on Periodic Graphs.” <i>European Journal of Applied Mathematics</i>, Cambridge University Press, 2024, pp. 1–29, doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>.","apa":"Portinale, L., &#38; Quattrocchi, F. (2024). Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. <i>European Journal of Applied Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0956792524000810\">https://doi.org/10.1017/s0956792524000810</a>","short":"L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics (2024) 1–29.","chicago":"Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits of Optimal Transport with Linear Growth on Periodic Graphs.” <i>European Journal of Applied Mathematics</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/s0956792524000810\">https://doi.org/10.1017/s0956792524000810</a>.","ama":"Portinale L, Quattrocchi F. Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. <i>European Journal of Applied Mathematics</i>. 2024:1-29. doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>","ista":"Portinale L, Quattrocchi F. 2024. Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. European Journal of Applied Mathematics., 1–29."},"acknowledgement":"L.P. gratefully acknowledges fundings from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1, Projekt-ID 390685813. F.Q. gratefully acknowledges support from the Austrian Science Fund (FWF) project 10.55776/F65.","abstract":[{"lang":"eng","text":"We prove discrete-to-continuum convergence for dynamical optimal transport on  Zd\r\n -periodic graphs with cost functional having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer, Maas, and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the convergence behaviour of discrete boundary-value dynamical transport problems is proved under the stronger assumption of superlinear growth. Our result extends the known literature to some important classes of examples, such as scaling limits of  1 -Wasserstein transport problems. Similarly to what happens in the quadratic case, the geometry of the graph plays a crucial role in the structure of the limit cost function, as we discuss in the final part of this work, which includes some visual representations."}],"publication_status":"epub_ahead","OA_type":"gold","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.1017/S0956792524000810","open_access":"1"}],"status":"public","day":"20"}