Mathematical analysis/Functional analysis
A certain weighted variant of the embedding inequalities
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 663-668.

In this Note, for vector functions defined on unbounded domains of R3, we consider continuous embeddings of weighted homogeneous Sobolev spaces into weighted Lebesgue spaces. Sufficient conditions on power-type weights for the validity of the inequalities are investigated. Moreover, the related properties of the suitable approximation by smooth functions with a bounded support can be proved.

Dans cette Note, pour des fonctions vectorielles définies sur des domaines non bornés de R3, nous considérons des inégalités dʼinjection dʼespaces de Sobolev homogènes avec poids dans des espaces de Lebesgue avec poids. Des conditions suffisantes pour justifier ces inégalités sont établies dans le cas de poids de type puissance. En outre, nous vérifions les propriétés dʼapproximation par des fonctions indéfiniment différentiables à support borné.

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DOI: 10.1016/j.crma.2013.07.008
Kračmar, Stanislav 1; Nečasová, Šárka 2; Penel, Patrick 3

1 Czech Technical University, Technical Mathematics, Karlovo náměsti 13, 121 35 Praha 2, Czech Republic
2 Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 115 67 Praha 1, Czech Republic
3 Université du Sud, Toulon–Var, Mathématique, BP 20132, 83957 La Garde cedex, France
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Kračmar, Stanislav; Nečasová, Šárka; Penel, Patrick. A certain weighted variant of the embedding inequalities. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 663-668. doi : 10.1016/j.crma.2013.07.008. http://www.numdam.org/articles/10.1016/j.crma.2013.07.008/

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