@article{18706,
  abstract     = {We prove discrete-to-continuum convergence for dynamical optimal transport on  Zd
 -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.},
  author       = {Portinale, Lorenzo and Quattrocchi, Filippo},
  issn         = {1469-4425},
  journal      = {European Journal of Applied Mathematics},
  keywords     = {optimal transport, discrete-to-continuum, homogenisation, linear growth, gamma-convergence},
  number       = {3},
  pages        = {614--642},
  publisher    = {Cambridge University Press},
  title        = {{Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs}},
  doi          = {10.1017/s0956792524000810},
  volume       = {37},
  year         = {2026},
}