no. 5-6
Partial Differential Equations/Functional Analysis
On Hardy inequalities with singularities on the boundary
[Sur les inégalités de Hardy avec des singularités sur la frontière]

Présenté par : the Editorial Board

Cazacu, Cristian1, 2
1 BCAM – Basque Center for Applied Mathematics, Bizkaia Technology Park 500, 48160 Derio, Basque Country, Spain
2 Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 273-277.

Dans ce travail nous présentons quelques inégalités de Hardy–Poincaré avec une singularité localisée sur la frontière dʼun domaine régulier. Ensuite, nous considérons des domaines coniques en dimension N⩾3 dont le sommet est sur la singularité et nous établissons des bornes supérieure et inférieure pour les constantes optimales correspondantes dans lʼinégalité de Hardy. En particulier, nous montrons le comportement asymptotique de la constante optimale lorsque lʼamplitude du cône tend vers zéro.

In this Note we present some Hardy–Poincaré inequalities with one singularity localized on the boundary of a smooth domain. Then, we consider conical domains in dimension N⩾3 whose vertex is on the singularity and we show upper and lower bounds for the corresponding optimal constants in the Hardy inequality. In particular, we prove the asymptotic behavior of the optimal constant when the amplitude of the cone tends to zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.02.005
Cazacu, Cristian 1, 2

1 BCAM – Basque Center for Applied Mathematics, Bizkaia Technology Park 500, 48160 Derio, Basque Country, Spain
2 Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain 
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Cazacu, Cristian. On Hardy inequalities with singularities on the boundary. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 273-277. doi : 10.1016/j.crma.2011.02.005. http://www.numdam.org/articles/10.1016/j.crma.2011.02.005/

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