Extremal functions for the anisotropic Sobolev inequalities
El Hamidi, A. ; Rakotoson, J. M.
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 741-756 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2007__24_5_741_0,
     author = {El Hamidi, A. and Rakotoson, J. M.},
     title = {Extremal functions for the anisotropic Sobolev inequalities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {741-756},
     doi = {10.1016/j.anihpc.2006.06.003},
     mrnumber = {2348050},
     zbl = {pre05228820},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_5_741_0}
}

El Hamidi, A.; Rakotoson, J. M. Extremal functions for the anisotropic Sobolev inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 741-756. doi : 10.1016/j.anihpc.2006.06.003. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_5_741_0/

[1] Aubin T., Problèmes isopérimètriques et espaces de Sobolev, J. Differential Geometry 11 (4) (1976) 573-598. | MR 448404 | Zbl 0371.46011

[2] Brezis H., Lieb E., A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR 699419 | Zbl 0526.46037

[3] El Hamidi A., Rakotoson J.M., Compactness and quasilinear problems with critical exponents, Differential Integral Equations 18 (2005) 1201-1220. | MR 2174817

[4] Fragala I., Gazzola F., Kawohl B., Existence and nonexistence results for anisotropic quasilinear elliptic equation, Ann. I. H. Poincaré Anal. Non Lineairé 21 (2004) 715-734. | Numdam | MR 2086756 | Zbl pre02116186

[5] Lions P.L., The concentration-compactness principle in the calculus of variations. The limit case, part 1, Rev. Mat. Iberoamericana 1 (1) (1985) 145-201. | MR 834360 | Zbl 0704.49005

[6] Nikol'Skii S.M., On imbedding, continuation and approximation theorems for differentiable functions of several variables, Russian Math. Surveys 16 (1961) 55-104. | MR 149267 | Zbl 0117.29101

[7] Rakosnik J., Some remarks to anisotropic Sobolev spaces I, Beiträge zur Analysis 13 (1979) 55-68. | MR 536217 | Zbl 0399.46025

[8] Rakosnik J., Some remarks to anisotropic Sobolev spaces II, Beiträge zur Analysis 15 (1981) 127-140. | MR 614784 | Zbl 0494.46034

[9] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (4) (1976) 353-372. | MR 463908 | Zbl 0353.46018

[10] Troisi M., Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1969) 3-24. | MR 415302 | Zbl 0182.16802

[11] Ven'-Tuan L., On embedding theorems for spaces of functions with partial derivatives of various degrees of summability, Vestnik Leningrad Univ. 16 (1961) 23-37, (in Russian). | MR 143020 | Zbl 0100.31803

[12] Willem M., Minimax Theorems, Birkhäuser, 1996. | MR 1400007 | Zbl 0856.49001

[13] Yamabe H., On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960) 21-37. | MR 125546 | Zbl 0096.37201