Cette revue est la version écrite d’un exposé sur quelques résultats (d’après des travaux en collaboration avec J. Dolbeault, M. Loss, G. Tarantello and A. Tertikas) concernant les propriétés de symétrie des fonctions extrémales pour les inégalités de Caffarelli-Kohn-Nirenberg
@article{SLSEDP_2011-2012____A29_0, author = {Maria J. Esteban}, title = {Une revue sur quelques in\'egalit\'es fonctionnelles et les propri\'et\'es de sym\'etrie pour leurs fonctions extr\'emales}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:29}, pages = {1--13}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2011-2012}, doi = {10.5802/slsedp.23}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.23/} }
TY - JOUR AU - Maria J. Esteban TI - Une revue sur quelques inégalités fonctionnelles et les propriétés de symétrie pour leurs fonctions extrémales JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:29 PY - 2011-2012 SP - 1 EP - 13 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.23/ DO - 10.5802/slsedp.23 LA - fr ID - SLSEDP_2011-2012____A29_0 ER -
%0 Journal Article %A Maria J. Esteban %T Une revue sur quelques inégalités fonctionnelles et les propriétés de symétrie pour leurs fonctions extrémales %J Séminaire Laurent Schwartz — EDP et applications %Z talk:29 %D 2011-2012 %P 1-13 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.23/ %R 10.5802/slsedp.23 %G fr %F SLSEDP_2011-2012____A29_0
Maria J. Esteban. Une revue sur quelques inégalités fonctionnelles et les propriétés de symétrie pour leurs fonctions extrémales. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 29, 13 p. doi : 10.5802/slsedp.23. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.23/
[1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geometry, 11 (1976), pp. 573–598. | MR | Zbl
[2] W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. (2), 138 (1993), pp. 213–242. | MR | Zbl
[3] M.-F. Bidaut-Véron and L. Véron, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math., 106 (1991), pp. 489–539. | MR | Zbl
[4] L. Caffarelli, R. Kohn, and L. Nirenberg, First order interpolation inequalities with weights, Compositio Math., 53 (1984), pp. 259–275. | Numdam | MR | Zbl
[5] F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities : sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math., 54 (2001), pp. 229–258. | MR | Zbl
[6] K. S. Chou and C. W. Chu, On the best constant for a weighted Sobolev-Hardy inequality, J. London Math. Soc. (2), 48 (1993), pp. 137–151. | MR | Zbl
[7] M. Del Pino, J. Dolbeault, S. Filippas, and A. Tertikas, A logarithmic Hardy inequality, Journal of Functional Analysis, 259 (2010), pp. 2045 – 2072. | MR | Zbl
[8] J. Dolbeault, M. J. Esteban, and M. Loss, Symmetry of extremals of functional inequalities via spectral estimates for linear operators, To appear in J. Math. Physics, (2012). | MR
[9] J. Dolbeault, M. J. Esteban, M. Loss, and G. Tarantello, On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities, Adv. Nonlinear Stud., 9 (2009), pp. 713–726. | MR | Zbl
[10] J. Dolbeault, M. J. Esteban, and G. Tarantello, The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 7 (2008), pp. 313–341. | Numdam | MR | Zbl
[11] J. Dolbeault, M. J. Esteban, G. Tarantello, and A. Tertikas, Radial symmetry and symmetry breaking for some interpolation inequalities, To appear in Calculus of Variations and PDE, (2011). | MR | Zbl
[12] V. Felli and M. Schneider, Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type, J. Differential Equations, 191 (2003), pp. 121–142. | MR | Zbl
[13] V. Glaser, A. Martin, H. Grosse, and W. Thirring, A family of optimal conditions for the absence of bound states in a potential, Essays in Honor of Valentine Bargmann, E. Lieb, B. Simon, A. Wightman Eds. Princeton University Press, 1976, pp. 169–194. | Zbl
[14] T. Horiuchi, Best constant in weighted Sobolev inequality with weights being powers of distance from the origin, J. Inequal. Appl., 1 (1997), pp. 275–292. | MR | Zbl
[15] J. B. Keller, Lower bounds and isoperimetric inequalities for eigenvalues of the Schrödinger equation, J. Mathematical Phys., 2 (1961), pp. 262–266. | MR | Zbl
[16] E. Lieb and W. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, Essays in Honor of Valentine Bargmann, E. Lieb, B. Simon, A. Wightman Eds. Princeton University Press, 1976, pp. 269–303. | Zbl
[17] E. H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. (2), 118 (1983), pp. 349–374. | MR | Zbl
[18] C.-S. Lin and Z.-Q. Wang, Erratum to : “Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities” [Proc. Amer. Math. Soc. 132 (2004), no. 6, 1685–1691], Proc. Amer. Math. Soc., 132 (2004), p. 2183. | MR | Zbl
[19] P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), pp. 109–145. | Numdam | MR | Zbl
[20] Idem, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), pp. 223–283. | Numdam | MR | Zbl
[21] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4), 110 (1976), pp. 353–372. | MR | Zbl
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