Sharp Hardy–Sobolev inequalities

Filippas, S.; Maz'ya, V.G.; Tertikas, A.

doi:10.1016/j.crma.2004.07.023

Partial Differential Equations

Sharp Hardy–Sobolev inequalities
[Inégalités de Hardy–Sobolev précisées.]

Présenté par : Haïm Brezis

Filippas, S.^1,² ; Maz'ya, V.G.^3,⁴ ; Tertikas, A.^2,⁵

¹ Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece
² Institute of Applied and Computational Mathematics FORTH, 71110 Heraklion, Greece
³ Department of Mathematics, Ohio State University, Columbus, OH 43210, USA
⁴ Department of Mathematics, Linkoeping University, 58183 Linkoeping, Sweden
⁵ Department of Mathematics, University of Crete, 71409 Heraklion, Greece

Comptes Rendus. Mathématique, Tome 339 (2004) no. 7, pp. 483-486.

Résumé
Abstract

Soit Ω un ouvert borné et regulier dans $R^{N}$ , $N ⩾ 3$ . On montre que l'inegalité de Hardy, liée à la distance au bord, avec meilleure constante ( $\frac{1}{4}$ ), peut être améliorée en ajoutant un multiple de la norme de Sobolev critique.

Let Ω be a smooth bounded domain in $R^{N}$ , $N ⩾ 3$ . We show that Hardy's inequality involving the distance to the boundary, with best constant ( $\frac{1}{4}$ ), may still be improved by adding a multiple of the critical Sobolev norm.

Reçu le : 2004-07-26
Publié le : 2004-09-25

DOI : 10.1016/j.crma.2004.07.023

Affiliations des auteurs :

Filippas, S. ^{1, 2} ; Maz'ya, V.G. ^{3, 4} ; Tertikas, A. ^{2, 5}

@article{CRMATH_2004__339_7_483_0,
     author = {Filippas, S. and Maz'ya, V.G. and Tertikas, A.},
     title = {Sharp {Hardy{\textendash}Sobolev} inequalities},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {483--486},
     publisher = {Elsevier},
     volume = {339},
     number = {7},
     year = {2004},
     doi = {10.1016/j.crma.2004.07.023},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2004.07.023/}
}

TY  - JOUR
AU  - Filippas, S.
AU  - Maz'ya, V.G.
AU  - Tertikas, A.
TI  - Sharp Hardy–Sobolev inequalities
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 483
EP  - 486
VL  - 339
IS  - 7
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2004.07.023/
DO  - 10.1016/j.crma.2004.07.023
LA  - en
ID  - CRMATH_2004__339_7_483_0
ER  -

%0 Journal Article
%A Filippas, S.
%A Maz'ya, V.G.
%A Tertikas, A.
%T Sharp Hardy–Sobolev inequalities
%J Comptes Rendus. Mathématique
%D 2004
%P 483-486
%V 339
%N 7
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2004.07.023/
%R 10.1016/j.crma.2004.07.023
%G en
%F CRMATH_2004__339_7_483_0

Filippas, S.; Maz'ya, V.G.; Tertikas, A. Sharp Hardy–Sobolev inequalities. Comptes Rendus. Mathématique, Tome 339 (2004) no. 7, pp. 483-486. doi : 10.1016/j.crma.2004.07.023. http://www.numdam.org/articles/10.1016/j.crma.2004.07.023/

Bibliographie
Cité par

[1] Barbatis, G.; Filippas, S.; Tertikas, A. A unified approach to improved $L^{p}$ Hardy inequalities with best constants, Trans. Amer. Math. Soc., Volume 356 (2004) no. 6, pp. 2169-2196

[2] Brezis, H.; Marcus, M. Hardy's inequalities revisited, Ann. Scuola Norm. Pisa, Volume 25 (1997), pp. 217-237

[3] Dávila, J.; Dupaigne, L. Hardy-type inequalities, J. Eur. Math. Soc., Volume 6 (2004) no. 3, pp. 335-365

[4] S. Filippas, V.G. Maz'ya, A. Tertikas, Critical Hardy Sobolev inequalities, in preparation

[5] Filippas, S.; Tertikas, A. Optimizing improved Hardy inequalities, J. Funct. Anal., Volume 192 (2002), pp. 186-233

[6] Maz'ya, V.G. Sobolev Spaces, Springer, 1985

[7] Vázquez, J.L.; Zuazua, E. The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal., Volume 173 (2000), pp. 103-153

Cité par Sources :