EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 27 (2021) Supplement ESAIM: COCV, 27 (2021) S3 References
Free Access
Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S3
Number of page(s) 29
DOI https://doi.org/10.1051/cocv/2020054
Published online 01 March 2021
  1. E. Abreu and L.G. Fernandes, On existence and nonexistence of isoperimetric inequalities with different monomial weights. Preprint arXiv:1904.01441v2 (2019). [Google Scholar]
  2. A. Alvino, F. Brock, F. Chiacchio, A. Mercaldo and M.R. Posteraro, Some isoperimetric inequalities on ℝN with respect to weights |x|α. J. Math. Anal. Appl. 451 (2017) 280–318. [Google Scholar]
  3. A. Alvino, F. Brock, F. Chiacchio, A. Mercaldo and M.R. Posteraro, On weighted isoperimetric inequalities with non-radial densities. Appl. Anal. 98 (2019) 1935–1945. [Google Scholar]
  4. A. Alvino, F. Brock, F. Chiacchio, A. Mercaldo and M.R. Posteraro, The isoperimetric problem for a class of non-radial weights and applications. J. Differ. Equ. 267 (2019) 6831–6871. [Google Scholar]
  5. V. Bayle, A. Cañete, F. Morgan and C. Rosales, On the isoperimetric problem in Euclidean space with density. Calc. Var. PDE 31 (2008) 27–46. [Google Scholar]
  6. M.F. Betta, F. Brock, A. Mercaldo and M.R. Posteraro, A weighted isoperimetric inequality and applications to symmetrization. J. Inequal. Appl. 4 (1999) 215–240. [Google Scholar]
  7. M.F. Betta, F. Brock, A. Mercaldo and M.R. Posteraro, Weighted isoperimetric inequalities on ℝN and applications to rearrangements. Math. Nachr. 281 (2008) 466–498. [Google Scholar]
  8. W. Boyer, B. Brown, G. Chambers, A. Loving and S. Tammen, Isoperimetric regions in ℝn with density rp. Anal. Geom. Metr. Spaces 4 (2016) 236–265. [Google Scholar]
  9. B. Brandolini, F. Della Pietra, C. Nitsch and C. Trombetti, Symmetry breaking in a constrained Cheeger type isoperimetric inequality. ESAIM: COCV 21 (2015) 359–371. [CrossRef] [EDP Sciences] [Google Scholar]
  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer (2010). [CrossRef] [Google Scholar]
  11. F. Brock, F. Chiacchio and A. Mercaldo, A weighted isoperimetric inequality in an orthant. Potential Anal. 41 (2012) 171–186. [Google Scholar]
  12. F. Brock, A. Mercaldo and M.R. Posteraro, On isoperimetric inequalities with respect to infinite measures. Rev. Mat. Iberoamericana 29 (2013) 665–690. [Google Scholar]
  13. D. Bucurand I. Fragalà, Proof of the honeycomb asymptotics for optimal Cheeger clusters. Adv. Math. 350 (2019) 97–129. [CrossRef] [Google Scholar]
  14. D. Bucurand I. Fragalà, A Faber-Krahn inequality for the Cheeger constant of N-gons. J. Geom. Anal. 26 (2016) 88–117. [Google Scholar]
  15. X. Cabre and X. Ros-Oton, Sobolev and isoperimetric inequalities with monomial weights. J. Differ. Equ. 255 (2013) 4312–4336. [Google Scholar]
  16. X. Cabre, X. Ros-Oton and J. Serra, Euclidean balls solve some isoperimetric problems with nonradial weights. C. R. Math. Acad. Sci. Paris 350 (2012) 945–947. [Google Scholar]
  17. A. Cañete, M. Miranda Jr. and D. Vittone, Some isoperimetric problems in planes with density. J. Geom. Anal. 20 (2010) 243–290. [Google Scholar]
  18. T. Carroll, A. Jacob, C. Quinn and R. Walters, The isoperimetric problem on planes with density. Bull. Aust. Math. Soc. 78 (2008) 177–197. [Google Scholar]
  19. V. Caselles, M. Miranda jr and M. Novaga, Total variation and Cheeger sets in Gauss space. J. Funct. Anal. 259 (2010) 1491–1516. [Google Scholar]
  20. H. Castro. Hardy-Sobolev inequalities with monomial weights. Ann. Mat. Pura Appl. 196 (2017) 579–598. [Google Scholar]
  21. G.R. Chambers, Proof of the Log-Convex Density Conjecture. J. Eur. Math. Soc. 21 (2019) 2301–2332. [Google Scholar]
  22. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian. Problems in analysis: A symposium in honor of Salomon Bochner (1970) 195–199. [Google Scholar]
  23. G. Csató, An isoperimetric problem with density and the Hardy Sobolev inequality in ℝ2. Differ. Int. Equ. 28 (2015) 971–988. [Google Scholar]
  24. J. Dahlberg, A. Dubbs, E. Newkirk and H. Tran, Isoperimetric regions in the plane with density rp . New York J. Math. 16 (2010) 31–51. [Google Scholar]
  25. G. De Philippis, G. Franzina and A. Pratelli, Existence of isoperimetric sets with densities “converging from below” on ℝN. J. Geom. Anal. 27 (2017) 1086–1105. [Google Scholar]
  26. L. Di Giosia, J. Habib, L. Kenigsberg, D. Pittman and W. Zhu, Balls Isoperimetric in ℝn with Volume and Perimeter Densities rm and rk . Preprint arXiv:1610.05830v2 (2019). [Google Scholar]
  27. A. Diaz, N. Harman, S. Howe and D. Thompson, Isoperimetric problems in sectors with density. Adv. Geom. 12 (2012) 589–619. [Google Scholar]
  28. V. Franceschi, A minimal partition problem with trace constraint in the Grushin plane. Calc. Var. Partial Differ. Equ. 56 (2017) 104. [Google Scholar]
  29. V. Franceschi and R. Monti, Isoperimetric problem in H-type groups and Grushin spaces. Rev. Mat. Iberoam. 32 (2016) 1227–1258. [CrossRef] [Google Scholar]
  30. V. Franceschi and G. Stefani, Symmetric double bubbles in the Grushin plane. ESAIM: COCV 25 (2019) 37. [EDP Sciences] [Google Scholar]
  31. P. Gurka and B. Opic, Continuous and compact imbeddings of weighted Sobolev spaces II. Czechoslovak Math. J. 39 (1989) 78–94. [Google Scholar]
  32. N. Harman, S. Howe and F. Morgan, Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Rev. Mat. Iberoamericana 27 (2011) 909–918. [Google Scholar]
  33. S. Howe, The Log-Convex Density Conjecture and vertical surface area in warped products. Adv. Geom. 15 (2015) 455–468. [Google Scholar]
  34. I.R. Ionescu and T. Lachand-Robert, Generalized Cheeger sets related to landslides. Calc. Var. Partial Differ. Equ. 23 (2005) 227–249. [Google Scholar]
  35. B. Kawohl and V. Fridman, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant. Comment. Math. Univ. Carolin. 44 (2003) 659–667. [Google Scholar]
  36. A.V. Kolesnikov and R.I. Zhdanov, On isoperimetric sets of radially symmetric measures. Concentration, functional inequalities and isoperimetry In Vol. 545 of Contemp. Math. Amer. Math. Soc., Providence, RI (2011) 123–154. [Google Scholar]
  37. C. Maderna and S. Salsa. Sharp estimates for solutions to a certain type of singular elliptic boundary value problems in two dimensions. Applicable Analysis 12 (1981) 307–321. [Google Scholar]
  38. V. Maz’ja, Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces. Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002). In Vol. 338 of Contemp. Math. Amer. Math. Soc., Providence, RI (2003) 307–340. [Google Scholar]
  39. V. Maz’ja and T. Shaposhnikova, A collection of sharp dilation invariant integral inequalities for differentiable functions. Sobolev spaces in mathematics I. In Vol. 8 of Int. Math. Ser. (N.Y.). Springer (2009) 223–247. [Google Scholar]
  40. R. Monti and D. Morbidelli, Isoperimetric inequality in the Grushin plane. J. Geom. Anal. 14 (2004) 355–368. [Google Scholar]
  41. F. Morgan, Manifolds with density. Notices Amer. Math. Soc. 52 (2005) 853–858. [Google Scholar]
  42. F. Morgan, The Log-Convex Density Conjecture. Contemp. Math. 545 (2011) 209–211. [Google Scholar]
  43. F. Morgan and A. Pratelli, Existence of isoperimetric regions in ℝN with density. Ann. Global Anal. Geom. 43 (2013) 331–365. [Google Scholar]
  44. E. Parini, An introduction to the Cheeger problem. Surv. Math. Appl. 6 (2011) 9–21. [Google Scholar]
  45. A. Pratelli and G. Saracco, On the isoperimetric problem with double density. Nonlinear Anal. 177 (2018) 733–752. [CrossRef] [Google Scholar]
  46. A. Pratelli and G. Saracco, The ε − εβ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets. Adv. Nonlinear Stud. 20 (2020) 539–555. [Google Scholar]
  47. G. Saracco, Weighted Cheeger sets are domains of isoperimetry. Manuscripta Math. 156 (2018) 371–381. [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.