---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '18706'
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."
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.
article_processing_charge: Yes
article_type: original
author:
- first_name: Lorenzo
  full_name: Portinale, Lorenzo
  id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
  last_name: Portinale
- first_name: Filippo
  full_name: Quattrocchi, Filippo
  id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
  last_name: Quattrocchi
  orcid: 0009-0000-9773-1931
citation:
  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>
  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>.
  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.
  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>.
  short: L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics 37
    (2026) 614–642.
das_tickbox: '0'
date_created: 2024-12-23T11:03:59Z
date_published: 2026-06-01T00:00:00Z
date_updated: 2026-08-26T22:31:04Z
day: '01'
ddc:
- '500'
department:
- _id: GradSch
- _id: JaMa
doi: 10.1017/s0956792524000810
external_id:
  isi:
  - '001381435800001'
file:
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  checksum: d038f4d00cbfbde2672c17138eab21c9
  content_type: application/pdf
  creator: dernst
  date_created: 2026-07-23T05:55:03Z
  date_updated: 2026-07-23T05:55:03Z
  file_id: '22386'
  file_name: 2026_EuropJourAppliedMath_Portinale.pdf
  file_size: 612317
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file_date_updated: 2026-07-23T05:55:03Z
has_accepted_license: '1'
intvolume: '        37'
isi: 1
issue: '3'
keyword:
- optimal transport
- discrete-to-continuum
- homogenisation
- linear growth
- gamma-convergence
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 614-642
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication: European Journal of Applied Mathematics
publication_identifier:
  eissn:
  - 1469-4425
  issn:
  - 0956-7925
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
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    status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Discrete-to-continuum limits of optimal transport with linear growth on periodic
  graphs
tmp:
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  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
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...