EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 57 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 57
Number of page(s) 32
DOI https://doi.org/10.1051/cocv/2026034
Published online 14 July 2026
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zurich, 2nd edn. Birkhauser Verlag, Basel (2008). [Google Scholar]
  2. G. Peyré, M. Cuturi et al., Computational optimal transport: with applications to data science. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  3. C. Villani et al., Optimal Transport: Old and New, vol. 338. Springer (2009). [Google Scholar]
  4. A. Delalande, Quantitative Stability in Quadratic Optimal Transport. PhD thesis, Universite Paris-Saclay (2022). [Google Scholar]
  5. Q. Mérigot, A. Delalande and F. Chazal, Quantitative stability of optimal transport maps and linearization of the 2-wasserstein space, in Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, vol. 108 of Proceedings of Machine Learning Research, edited by S. Chiappa and R. Calandra. PMLR (2020) 3186–3196. [Google Scholar]
  6. N. Gigli, On Hölder continuity-in-time of the optimal transport map towards measures along a curve. Proc. Edinb. Math. Soc. 54 (2011) 401–409. [Google Scholar]
  7. L.A. Caffarelli, The regularity of mappings with a convex potential. J. Am. Math. Soc. 5 (1992) 99–104. [CrossRef] [Google Scholar]
  8. A. Gallouët, Q. Mérigot and B. Thibert, Strong c-concavity and stability in optimal transport. J. Math. Pures Appl. 205 (2026) 103773. [Google Scholar]
  9. M. Neilan and W. Zhang, Rates of convergence in norm for the Monge–Ampère equation. SIAM J. Numer. Anal. 56 (2018) 3099–3120. [Google Scholar]
  10. R.J Berman, Convergence rates for discretized monge–ampere equations and quantitative stability of optimal transport. Found. Computat. Math. 21 (2021) 1099–1140. [CrossRef] [Google Scholar]
  11. W. Li and R.H. Nochetto, Quantitative stability and error estimates for optimal transport plans. IMA J. Numer. Anal. 41 (2021) 1941–1965. [Google Scholar]
  12. A. Delalande and Q. Merigot, Quantitative stability of optimal transport maps under variations of the target measure. Duke Math. J. 172 (2023) 3321–3357. [Google Scholar]
  13. V. Divol, J. Niles-Weed and A.-A. Pooladian, Tight stability bounds for entropic Brenier maps. Int. Math. Res. Notices 2025 (2025), rnaf078, https://doi.org/10.1093/imrn/rnaf078. [Google Scholar]
  14. L. Chizat, A. Delalande and T. Vaškevičius, Sharper exponential convergence rates for Sinkhorn's algorithm in continuous settings. Math. Program. 215 (2026) 809–858. [Google Scholar]
  15. R. McCann, A Convexity Theory for Interacting Gases and Equilibrium Crystals. PhD Thesis, Princeton University (1994). [Google Scholar]
  16. H.J. Brascamp and E.H. Lieb, On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Funct. Anal. 22 (1976) 366–389. [Google Scholar]
  17. C. Letrouit and Q. Mérigot, Gluing methods for quantitative stability of optimal transport maps arXiv preprint arXiv:2411.04908 (2024). [Google Scholar]
  18. D. Cordero-Erausquin, R.J. McCann and M. Schmuckenschlager, Prékopa-leindler type inequalities on riemannian manifolds, jacobi fields, and optimal transport, in Annales de la Faculté des sciences de Toulouse: Mathématiques, vol. 15 (2006) 613–635. [Google Scholar]
  19. J. Kitagawa, C. Letrouit and Q. Mérigot, Stability of optimal transport maps on Riemannian manifolds (2025) arXiv preprint arXiv:2504.05412. [Google Scholar]
  20. R. Peyre, Comparison between W2 distance and H−1 norm, and localization of Wasserstein distance. ESAIM Control Optim. Calc. Var. 24 (2018) 1489–1501. [Google Scholar]
  21. L. Ambrosio, F. Stra and D. Trevisan, A PDE approach to a 2-dimensional matching problem. Probab. Theory Related Fields 173 (2019) 433–477. [Google Scholar]
  22. M. Ledoux, On optimal matching of Gaussian samples. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 457 (2017) 226–264. [Google Scholar]
  23. S. Di Marino and A. Gerolin, An optimal transport approach for the schrödinger bridge problem and convergence of sinkhorn algorithm. J. Sci. Comput. 85 (2020) 27. [Google Scholar]
  24. M. Nutz and J. Wiesel, Entropic optimal transport: convergence of potentials. Probab. Theory Related Fields 184 (2022) 401–424. [Google Scholar]
  25. H. Brezis and P. Mironescu, Gagliardo–Nirenberg inequalities and non-inequalities: the full story. Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018) 1355–1376. [Google Scholar]
  26. A. Figalli and N. Gigli, A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. J. Math. Pures Appl. 94 (2010) 107–130. [Google Scholar]
  27. P. Lindqvist, Notes on the Stationary p-Laplace Equation. Springer (2019). [Google Scholar]
  28. K. Shashiashvili and M. Shashiashvili, Estimation of the derivative of the convex function by means of its uniform approximation. J. Inequal. Pure Appl. Math. 6 (2005) 1–10. [Google Scholar]
  29. S. Hussain, J. Pečarić and M. Shashiashvili, The weighted square integral inequalities for the first derivative of the function of a real variable. J. Inequal. Appl. 2008 (2008) 1–14. [Google Scholar]
  30. J. Pečarić, M. Shoaib Saleem, H. Ur Rehman, A.M. Nizami and A. Hussain, Reverse poincaré-type inequalities for the difference of superharmonic functions. J. Inequal. Appl. 2015 (2015) 1–11. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.