Comptes Rendus
Partial Differential Equations
Sharp Hardy–Sobolev inequalities
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 483-486.

Let Ω be a smooth bounded domain in RN, N3. We show that Hardy's inequality involving the distance to the boundary, with best constant (14), may still be improved by adding a multiple of the critical Sobolev norm.

Soit Ω un ouvert borné et regulier dans RN, N3. On montre que l'inegalité de Hardy, liée à la distance au bord, avec meilleure constante (14), peut être améliorée en ajoutant un multiple de la norme de Sobolev critique.

Received:
Published online:
DOI: 10.1016/j.crma.2004.07.023
S. Filippas 1, 2; V.G. Maz'ya 3, 4; A. Tertikas 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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S. Filippas; V.G. Maz'ya; A. Tertikas. Sharp Hardy–Sobolev inequalities. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 483-486. doi : 10.1016/j.crma.2004.07.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.023/

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

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

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

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

[7] J.L. Vázquez; E. Zuazua 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

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