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

Abstract (VO)
Résumé

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.

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.

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}

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

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     title = {Sharp {Hardy{\textendash}Sobolev} inequalities},
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     pages = {483--486},
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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

Bibliographie
Cité par

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