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