Open Access
Volume 28, 2022
Article Number 37
Number of page(s) 20
Published online 14 June 2022
  1. E. Acerbi, N. Fusco and M. Morini, Minimality via second variation for a nonlocal isoperimetric problem. Commun. Math. Phys. 322 (2013) 515–557. [CrossRef] [Google Scholar]
  2. G. Buttazzo, G. Carlier and M. Laborde, On the Wasserstein distance between mutually singular measures. Adv. Calc. Var. 13 (2020) 141–154. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Carazzato, N. Fusco and A. Pratelli, Minimality of balls in the small volume regime for a general Gamow type functional (2020). [Google Scholar]
  4. F. Cavalletti and S. Farinelli, Indeterminacy estimates and the size of nodal sets in singular spaces. Adv. Math. 389 (2021) Paper No. 107919, 38. [CrossRef] [Google Scholar]
  5. R. Choksi, C.B. Muratov and I. Topaloglu, An old problem resurfaces nonlocally: Gamow’s liquid drops inspire today’s research and applications. Notices Amer. Math. Soc. 64 (2017) 1275–1283. [Google Scholar]
  6. M. Cicalese and G.P. Leonardi, A selection principle for the sharp quantitative isoperimetric inequality. Arch. Ration. Mech. Anal. 206 (2012) 617–643. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. De Philippis, A.R. Mészaros, F. Santambrogio and B. Velichkov, BV estimates in optimal transportation and applications. Arch. Rati. Mech. Anal. 219 (2015) 829–860. [Google Scholar]
  8. A. Figalli, N. Fusco, F. Maggi, V. Millot and M. Morini, Isoperimetry and stability properties of balls with respect to nonlocal energies. Commun. Math. Phys. 336 (2015) 441–507. [CrossRef] [Google Scholar]
  9. R.L. Frank and E.H. Lieb, A compactness lemma and its application to the existence of minimizers for the liquid drop model. SIAM J. Math. Anal. 47 (2015) 4436–4450. [Google Scholar]
  10. R.L. Frank and P.T. Nam, Existence and nonexistence in the liquid drop model (2021). [Google Scholar]
  11. B. Fuglede, Stability in the isoperimetric problem for convex or nearly spherical domains in Rn. Trans. Am. Math. Soc. 314 (1989). [Google Scholar]
  12. M. Goldman and M. Novaga, Volume-constrained minimizers for the prescribed curvature problem in periodic media. Calc. Var. Partial Differ. Equ. 44 (2012) 297–318. [CrossRef] [Google Scholar]
  13. M. Goldman, M. Novaga and B. Ruffini, Existence and stability for a non-local isoperimetric model of charged liquid drops. Arch. Ration. Mech. Anal. 217 (2015) 1–36. [CrossRef] [MathSciNet] [Google Scholar]
  14. H. Knupfer and C.B. Muratov, On an isoperimetric problem with a competing nonlocal term II: the general case. Commun. Pure Appl. Math. 67 (2014) 1974–1994. [CrossRef] [Google Scholar]
  15. H. Knupfer, C.B. Muratov and M. Novaga, Low density phases in a uniformly charged liquid. Commun. Math. Phys. 345 (2016) 141–183. [CrossRef] [Google Scholar]
  16. F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory, Cambridge Studies in Advanced Mathematics. Cambridge University Press (2012). [CrossRef] [Google Scholar]
  17. E. Mukoseeva and G. Vescovo, Minimality of the ball for a model of charged liquid droplets (2019). [Google Scholar]
  18. M. Novack, I. Topaloglu and R. Venkatraman, Least Wasserstein distance between disjoint shapes with perimeter regularization. Preprints arXiv:2108.04390 (2021). [Google Scholar]
  19. M. Novaga and A. Pratelli, Minimisers of a general Riesz-type problem. Nonlinear Anal. 209 (2021) Paper No. 112346, 27. [CrossRef] [Google Scholar]
  20. M. Pegon, Large mass minimizers for isoperimetric problems with integrable nonlocal potentials. Nonlinear Anal. 211 (2021) Paper No. 112395, 48. [CrossRef] [Google Scholar]
  21. M.A. Peletier and M. Roger, Partial localization, lipid bilayers, and the elastica functional. Arch. Ration. Mech. Anal. 193 (2009) 475–537. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Rigot, Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme. Mém. Soc. Math. Fr. (N.S.) (2000) vi+104. [Google Scholar]
  23. F. Santambrogio, Optimal transport for applied mathematicians. Vol. 87 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser/Springer, Cham (2015). [CrossRef] [Google Scholar]
  24. C. Villani, Topics in optimal transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]
  25. Q. Xia and B. Zhou, The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains. Adv. Calc. Variat. (2021) 000010151520200083. [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.