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All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 4 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 4
Number of page(s) 53
DOI https://doi.org/10.1051/cocv/2021106
Published online 11 January 2022
  1. L. Ambrosio, Lecture notes on optimal transport problems, in Mathematical Aspects of Evolving Interfaces. Springer (2003) 1–52. [Google Scholar]
  2. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons (2013). [Google Scholar]
  3. M. Bonacini and R. Cristoferi, Local and global minimality results for a nonlocal isoperimetric problem on ℝN. SIAM J. Math. Anal. 46 (2014) 2310–2349. [CrossRef] [MathSciNet] [Google Scholar]
  4. T.J.I. Bromwich, An Introduction to the Theory of Infinite Series. Vol. 335. Merchant Books (1908). [Google Scholar]
  5. A. Burchard, Cases of equality in the Riesz rearrangement inequality. Ann. Math. (1996) 499–527. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Burchard and G.R. Chambers, Geometric stability of the Coulomb energy. Calc. Variat. Partial Differ. Equ. 54 (2015) 3241–3250. [CrossRef] [Google Scholar]
  7. A. Burchard, R. Choksi and I. Topaloglu, Nonlocal shape optimization via interactions of attractive and repulsive potentials. Indiana Univ. Math. J. 67 (2018) 375–395. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Choksi, R.C. Fetecau and I. Topaloglu, On minimizers of interaction functionals with competing attractive and repulsive potentials, vol. 32 of Annales de l’Institut Henri Poincare (C) Non Linear Analysis. Elsevier (2015) 1283–1305. [CrossRef] [Google Scholar]
  9. R. Choksi, C.B. Muratov and I. Topaloglu, An old problem resurfaces nonlocally: Gamow’s liquid drops inspire today’s research and applications. Notic. AMS 64 (2017) 1275–1283. [Google Scholar]
  10. R. Choksi and M.A. Peletier, Small volume-fraction limit of the diblock copolymer problem: II. Diffuse-interface functional. SIAM J. Math. Anal. 43 (2011) 739–763. [Google Scholar]
  11. M. Christ, A sharpened Riesz-Sobolev inequality. Preprint arXiv:1706.02007 (2017). [Google Scholar]
  12. M. Cicalese and G.P. Leonardi, A selection principle for the sharp quantitative isoperimetric inequality. Arch. Ratl. Mech. Anal. 206 (2012) 617–643. [CrossRef] [Google Scholar]
  13. M. Cozzi and A. Figalli, Regularity theory for local and nonlocal minimal surfaces: an overview, in Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions. Springer (2017) 117–158. [CrossRef] [Google Scholar]
  14. C. Dellacherie and P.-A. Meyer, Probabilities and potential. Bull. Am. Math. Soc. 2 (1980) 510–514. [CrossRef] [Google Scholar]
  15. R. Estrada, The Funk-Hecke formula, harmonic polynomials, and derivatives of radial distributions. Boletim da Sociedade Paranaense de Matemática 37 (2017) 143–157. [CrossRef] [Google Scholar]
  16. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press (2015). [Google Scholar]
  17. F. Ferrari, Weyl and Marchaud derivatives: a forgotten history. Mathematics 6 (2018) 6. [CrossRef] [Google Scholar]
  18. 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]
  19. R. Frank, E. Lieb and R. Seiringer, Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J. Am. Math. Soc. 21 (2008) 925–950. [Google Scholar]
  20. R.L. Frank, R. Killip and P.T. Nam, Nonexistence of large nuclei in the liquid drop model. Lett. Math. Phys. 106 (2016) 1033–1036. [CrossRef] [MathSciNet] [Google Scholar]
  21. 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. [CrossRef] [MathSciNet] [Google Scholar]
  22. R.L. Frank and E.H. Lieb, A note on a theorem of M. Christ. Preprint arXiv:1909.04598 (2019). [Google Scholar]
  23. R.L. Frank and E.H. Lieb, Proof of spherical flocking based on quantitative rearrangement inequalities. Preprint arXiv:1909.04595 (2019). [Google Scholar]
  24. R.L. Frank and P.T. Nam, Existence and nonexistence in the liquid drop model. Calc. Variat. Partial Differ. Equ. 60 (2021). [Google Scholar]
  25. R.L. Frank, P.T. Nam and H. Van Den Bosch, The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Commun. Pure Appl. Math. 71 (2018) 577–614. [CrossRef] [Google Scholar]
  26. B. Fuglede, Stability in the isoperimetric problem for convex or nearly spherical domains in ℝn. Trans. Am. Math. Soc. 314 (1989) 619–638. [Google Scholar]
  27. N. Fusco, The quantitative isoperimetric inequality and related topics. Bull. Math. Sci. 5 (2015) 517–607. [Google Scholar]
  28. N. Fusco and A. Pratelli, Sharp stability for the Riesz potential. ESAIM: COCV 26 (2020) 113. [CrossRef] [EDP Sciences] [Google Scholar]
  29. G. Gamow, Mass defect curve and nuclear constitution. Proc. Royal Soc. London A 126 (1930) 632–644. [Google Scholar]
  30. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products. Academic Press (2014). [Google Scholar]
  31. V. Julin, Isoperimetric problem with a Coulomb repulsive term. Indiana Univ. Math. J. (2014) 77–89. [CrossRef] [MathSciNet] [Google Scholar]
  32. H. Knüpfer and C.B. Muratov, On an isoperimetric problem with a competing nonlocal term I: the planar case. Commun. Pure Appl. Math. 66 (2013) 1129–1162. [CrossRef] [Google Scholar]
  33. H. Knüpfer 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]
  34. D.A. La Manna An isoperimetric problem with a Coulombic repulsion and attractive term. ESAIM: COCV 25 (2019) 14. [CrossRef] [EDP Sciences] [Google Scholar]
  35. P.-L. Lions, The concentration-compactness principle in the Calculus of Variations. The locally compact case. Part 1. Ann. l’Institut Henri Poincaré (C) Non Linear Analysis 1 (1984) 109–145. [CrossRef] [Google Scholar]
  36. J. Lu and F. Otto, Nonexistence of a minimizer for Thomas-Fermi-Dirac-von Weizsäcker model. Commun. Pure Appl. Math. 67 (2014) 1605–1617. [CrossRef] [Google Scholar]
  37. J. Lu and F. Otto, An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus. Preprint arXiv:1508.07172 (2015). [Google Scholar]
  38. R.E. Pfiefer, Maximum and minimum sets for some geometric mean values. J. Theor. Probab. 3 (1990) 169–179. [CrossRef] [Google Scholar]
  39. L. Pick, A. Kufner, O. John and S. Fucík, Function Spaces 1. Walter de Gruyter (2012). [CrossRef] [Google Scholar]
  40. F. Riesz, Sur une inegalite integarale. J. London Math. Soc. 1 (1930) 162–168. [CrossRef] [Google Scholar]
  41. B. Rubin, The inversion of fractional integrals on a sphere. Israel J. Math. 79 (1992) 47–81. [CrossRef] [MathSciNet] [Google Scholar]
  42. B. Rubin, Vol. 160 of Introduction to Radon transforms. Cambridge University Press (2015). [Google Scholar]
  43. S. Samko, Hypersingular Integrals and Their Applications. CRC Press (2001). [CrossRef] [Google Scholar]
  44. L.J. Slater, Generalized Hypergeometric Functions. Cambridge Univ. Press (1966). [Google Scholar]
  45. F.G. Tricomi, A. Erdélyi et al., The asymptotic expansion of a ratio of gamma functions. Pacific J. Math. 1 (1951) 133–142. [Google Scholar]
  46. C. Villani, Vol. 338 of Optimal Transport: Old and New. Springer Science & Business Media (2008). [Google Scholar]

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