[{"abstract":[{"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.","lang":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","year":"2026","has_accepted_license":"1","title":"Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs","intvolume":"        37","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"20563"}]},"publication":"European Journal of Applied Mathematics","file":[{"date_updated":"2026-07-23T05:55:03Z","file_name":"2026_EuropJourAppliedMath_Portinale.pdf","file_id":"22386","access_level":"open_access","checksum":"d038f4d00cbfbde2672c17138eab21c9","content_type":"application/pdf","file_size":612317,"date_created":"2026-07-23T05:55:03Z","success":1,"relation":"main_file","creator":"dernst"}],"month":"06","date_updated":"2026-10-27T23:31:03Z","researchdata_availability":"no","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.","issue":"3","supplementarymaterial":"no","das_tickbox":"0","type":"journal_article","article_processing_charge":"Yes","OA_type":"gold","PlanS_conform":"1","DOAJ_listed":"1","article_type":"original","date_published":"2026-06-01T00:00:00Z","publication_identifier":{"issn":["0956-7925"],"eissn":["1469-4425"]},"external_id":{"isi":["001381435800001"]},"keyword":["optimal transport","discrete-to-continuum","homogenisation","linear growth","gamma-convergence"],"file_date_updated":"2026-07-23T05:55:03Z","doi":"10.1017/s0956792524000810","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"quality_controlled":"1","isi":1,"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>, vol. 37, no. 3. Cambridge University Press, pp. 614–642, 2026.","short":"L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics 37 (2026) 614–642.","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, 2026. <a href=\"https://doi.org/10.1017/s0956792524000810\">https://doi.org/10.1017/s0956792524000810</a>.","apa":"Portinale, L., &#38; Quattrocchi, F. (2026). 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>","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>. 2026;37(3):614-642. doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>","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>, vol. 37, no. 3, Cambridge University Press, 2026, pp. 614–42, doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>.","ista":"Portinale L, Quattrocchi F. 2026. Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. European Journal of Applied Mathematics. 37(3), 614–642."},"page":"614-642","author":[{"full_name":"Portinale, Lorenzo","first_name":"Lorenzo","last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Filippo","full_name":"Quattrocchi, Filippo","orcid":"0009-0000-9773-1931","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","last_name":"Quattrocchi"}],"OA_place":"publisher","status":"public","publisher":"Cambridge University Press","date_created":"2024-12-23T11:03:59Z","day":"01","ddc":["500"],"_id":"18706","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","fulldoi":"https://doi.org/10.1017/s0956792524000810","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","oa":1,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"volume":37}]