EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 18 / No 3 (July-September 2012) ESAIM: COCV, 18 3 (2012) 693-711 References
Highlight
Free Access
Issue
ESAIM: COCV
Volume 18, Number 3, July-September 2012
Page(s) 693 - 711
DOI https://doi.org/10.1051/cocv/2011167
Published online 29 September 2011
  1. A.D. Alexandrov, Zur theorie der gemischten volumina von konvexen korpern III, Mat. Sb. 3 (1938) 27–46. [Google Scholar]
  2. V. Alexandrov, N. Kopteva and S.S. Kutateladze, Blaschke addition and convex polyedra. preprint, arXiv:math/0502345 (2005). [Google Scholar]
  3. C. Bianchini and P. Salani, Concavity properties for elliptic free boundary problems. Nonlinear Anal. 71 (2009) 4461–4470. [Google Scholar]
  4. C. Borell, Capacitary inequalities of the Brunn-Minkowki type. Math. Ann. 263 (1983) 179–184. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Borell, Greenian potentials and concavity. Math. Ann. 272 (1985) 155–160. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Brascamp and E. Lieb, On extension of the Brunn-Minkowski and Prékopa-Leindler inequality, including inequalities for log concave functions, and with an application to diffision equation. J. Funct. Anal. 22 (1976) 366–389. [CrossRef] [Google Scholar]
  7. F. Brock, V. Ferone and B. Kawohl, A Symmetry Problem in the Calculus of Variations, Calc. Var. Partial Differential Equations 4 (1996) 593–599. [Google Scholar]
  8. E.M. Bronshtein, Extremal H-convex bodies. Sibirsk Mat. Zh. 20 (1979) 412–415. [MathSciNet] [Google Scholar]
  9. D. Bucur, G. Buttazzo and A. Henrot, Minimization of λ2(Ω) with a perimeter constraint. Indiana Univ. Math. J. 58 (2009) 2709–2728. [CrossRef] [MathSciNet] [Google Scholar]
  10. L. Caffarelli, D. Jerison and E. Lieb, On the case of equality in the Brunn-Minkowski inequality for capacity. Adv. Math. 117 (1996) 193–207. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Campi and P. Gronchi, On volume product inequalities for convex sets. Proc. Amer. Math. Soc. 134 (2006) 2393–2402. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Colesanti, Brunn-Minkowski inequalities for variational functionals and related problems. Adv. Math. 194 (2005) 105–140. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Colesanti and P. Cuoghi, The Brunn-Minkowski inequality for the n-dimensional logarithmic capacity. Potential Anal. 22 (2005) 289–304 [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Colesanti and M. Fimiani, The Minkowski problem for the torsional rigidity. Indiana Univ. Math. J. 59 (2010) 1013–1040. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Colesanti and P. Salani, The Brunn-Minkowski inequality for p-capacity of convex bodies. Math. Ann. 327 (2003) 459–479. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Crasta and F. Gazzola, Some estimates of the minimizing properties of web functions, Calc. Var. Partial Differential Equations 15 (2002) 45–66. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Crasta, I. Fragalà and F. Gazzola, On a long-standing conjecture by Pólya-Szegö and related topics. Z. Angew. Math. Phys. 56 (2005) 763–782. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Figalli, F. Maggi and A. Pratelli, A refined Brunn-Minkowski inequality for convex sets. Ann. Inst. Henri Poincaré Anal. Non Linéaire 26 (2009) 2511–2519. [CrossRef] [MathSciNet] [Google Scholar]
  19. I. Fragalà, F. Gazzola and M. Pierre, On an isoperimetric inequality for capacity conjectured by Pólya and Szegö. J. Differ. Equ. 250 (2011) 1500–1520. [CrossRef] [Google Scholar]
  20. P. Freitas, Upper and lower bounds for the first Dirichlet eigenvalue of a triangle, Proc. Am. Math. Soc. 134 (2006) 2083–2089. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Gardner, The Brunn-Minkowski inequality. Bull. Am. Math. Soc. (N.S.) 39 (2002) 355–405. [Google Scholar]
  22. R.J. Gardner and D. Hartenstine, Capacities, surface area, and radial sums, Adv. Math. 221 (2009) 601–626. [CrossRef] [MathSciNet] [Google Scholar]
  23. P.R. Goodey and R. Schneider, On the intermediate area functions of convex bodies. Math. Z. 173 (1980) 185–194. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Grinberg and G. Zhang, Convolutions, transforms, and convex bodies. Proc. London Math. Soc. 78 (1999) 77–115. [CrossRef] [MathSciNet] [Google Scholar]
  25. H. Hadwiger, Konkave Eikörperfunktionale. Monatsh. Math. 59 (1955) 230–237. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Henrot and M. Pierre, Variation et Optimisation de Formes : une analyse géométrique, Mathématiques et Applications 48. Springer (2005). [Google Scholar]
  27. D. Jerison, A Minkowski problem for electrostatic capacity. Acta Math. 176 (1996) 1–47. [CrossRef] [MathSciNet] [Google Scholar]
  28. D. Jerison, The direct method in the calculus of variations for convex bodies. Adv. Math. 122 (1996) 262–279. [CrossRef] [MathSciNet] [Google Scholar]
  29. S.S. Kutateladze, One functional-analytical idea by Alexandrov in convex geometry. Vladikavkaz. Mat. Zh. 4 (2002) 50–55. [MathSciNet] [Google Scholar]
  30. S.S. Kutateladze, Pareto optimality and isoperimetry. preprint, arXiv:0902.1157v1 (2009). [Google Scholar]
  31. T. Lachand-Robert and M.A. Peletier, An example of non-convex minimization and an application to Newton’s problem of the body of least resistance. Ann. Inst. Henri Poincaré 18 (2001) 179–198. [Google Scholar]
  32. J. Lamboley and A. Novruzi, Polygons as optimal shapes with convexity constraint. SIAM J. Control Optim. 48 (2009/10) 3003–3025. [CrossRef] [MathSciNet] [Google Scholar]
  33. J. Lamboley, A. Novruzi and M. Pierre, Regularity and singularities of optimal convex shapes in the plane, preprint (2011). [Google Scholar]
  34. M. Lanza, de Cristoforis, Higher order differentiability properties of the composition and of the inversion operator. Indag. Math. N S 5 (1994) 457–482. [CrossRef] [MathSciNet] [Google Scholar]
  35. G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies 27. Princeton University Press, Princeton, N.J. (1951). [Google Scholar]
  36. Ch. Pommerenke, Univalent functions. Vandenhoeck and Ruprecht, Göttingen (1975). [Google Scholar]
  37. P. Salani, A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue. Adv. Math. 194 (2005) 67–86. [CrossRef] [MathSciNet] [Google Scholar]
  38. R. Schneider, Eine allgemeine Extremaleigenschaft der Kugel. Monatsh. Math. 71 (1967) 231–237. [CrossRef] [MathSciNet] [Google Scholar]
  39. R. Schneider, Convex bodies : the Brunn-Minkowski theory. Cambridge Univ. Press (1993). [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.