Free Access
Issue
ESAIM: COCV
Volume 20, Number 2, April-June 2014
Page(s) 315 - 338
DOI https://doi.org/10.1051/cocv/2013065
Published online 06 February 2014
  1. L. Ambrosio and P. Tilli, Topics on Analysis in Metric Spaces, vol. 25 of Oxford Lect. Series Math. Appl. Oxford University Press, Oxford (2004). [Google Scholar]
  2. A. Alvino, V. Ferone, P.-L. Lions and G. Trombetti, Convex symmetrization and applications. Ann. Institut Henri Poincaré Anal. Non Linéaire 14 (1997) 275–293. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Belloni and B. Kawohl, The pseudo p-Laplace eigenvalue problem and viscosity solution as p → ∞. ESAIM: COCV 10 (2004) 28–52. [CrossRef] [EDP Sciences] [Google Scholar]
  4. L. Brasco, G. De Philippis and B. Velichkov, Faber-Krahn inequalities in sharp quantitative form, preprint (2013), available at http://cvgmt.sns.it/paper/2161/ [Google Scholar]
  5. D. Bucur and G. Buttazzo, Variational Methods in Shape Optimization Problems, vol. 65 of Progress Nonlinear Differ. Eqs. Birkhäuser Verlag, Basel (2005). [Google Scholar]
  6. T. Carroll and J. Ratzkin, Interpolating between torsional rigidity and principal frequency. J. Math. Anal. Appl. 379 (2011) 818–826. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. DiBenedetto, C1 + α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983) 827–850. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. Ekeland, Convexity methods in Hamiltonian mechanics. Springer-Verlag (1990). [Google Scholar]
  9. L. Esposito and C. Trombetti, Convex symmetrization and Pólya-Szegő inequality. Nonlinear Anal. 56 (2004) 43–62. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Ferone and R. Volpicelli, Convex rearrangement: equality cases in the Pólya-Szegő inequality, Calc. Var. Partial Differ. Eqs. 21 (2004) 259–272. [Google Scholar]
  11. A. Figalli, F. Maggi and A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Invent. Math. 81 (2010) 167–211. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Flucher, Extremal functions for the Moser-Trudinger inequality in two dimensions. Comment. Math. Helv. 67 (1992) 471–497. [CrossRef] [MathSciNet] [Google Scholar]
  13. I. Fragalà, F. Gazzola and J. Lamboley, Sharp bounds for the p-torsion of convex planar domains, in Geometric Properties for Parabolic and Elliptic PDE’s, vol. 2 of Springer INdAM Series (2013) 97–115. [Google Scholar]
  14. G. Franzina, P. D. Lamberti, Existence and uniqueness for a p-Laplacian nonlinear eigenvalue problem. Electron. J. Differ. Eqs. (2010) 10. [Google Scholar]
  15. N. Fusco, F. Maggi and A. Pratelli, Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Ann. Sci. Norm. Super. Pisa Cl. Sci. 8 (2009) 51–71. [Google Scholar]
  16. A. Henrot, Extremum problems for eigenvalues of elliptic operators, Frontiers in Mathematics. Birkhäuser Verlag, Basel (2006). [Google Scholar]
  17. S. Kesavan, Symmetrization and applications, in vol. 3 of Series in Analysis. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2006). [Google Scholar]
  18. M.-T. Kohler-Jobin, Symmetrization with equal Dirichlet integrals. SIAM J. Math. Anal. 13 (1982), 153–161. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.-T. Kohler-Jobin, Une méthode de comparaison isopérimétrique de fonctionnelles de domaines de la physique mathématique. I. Une démonstration de la conjecture isopérimétrique Formula de Pólya et Szegő, Z. Angew. Math. Phys. 29 (1978) 757–766. [CrossRef] [MathSciNet] [Google Scholar]
  20. M.-T. Kohler-Jobin, Démonstration de l’inégalité isopérimétrique Formula , conjecturée par Pólya et Szegő. C.R. Acad. Sci. Paris Sér. A-B 281 (1975) A119–A121. [Google Scholar]
  21. G.M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Analysis. Theory, Methods & Appl. 12 (1988) 1203–1219. [Google Scholar]
  22. K.-C. Lin, Extremal functions for Moser’s inequality. Trans. Amer. Math. Soc. 348 (1996) 2663–2671. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Moser, A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J. 20 (1970/71) 1077–1092. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Pólya, G. Szegő, Isoperimetric inequalities in mathematical physics, in vol. 27 of Ann. Math. Studies. Princeton University Press, Princeton, N. J. (1951). [Google Scholar]
  25. R. Schneider, Convex bodies: the Brunn-Minkowski theory. Cambridge University Press (1993). [Google Scholar]
  26. G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa 3 (1976) 697–718. [Google Scholar]
  27. N.S. Trudinger, On imbeddings into Orlicz spaces and some applications. J. Math. Mech. 17 (1967), 473–483. [MathSciNet] [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.