On inequalities of Hardy-Sobolev type
نویسندگان
چکیده
منابع مشابه
On Inequalities of Hardy–sobolev Type
Hardy–Sobolev–type inequalities associated with the operator L := x · ∇ are established, using an improvement to the Sobolev embedding theorem obtained by M. Ledoux. The analysis involves the determination of the operator semigroup {e−tL∗L}t>0.
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Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...
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1.1. Hardy-Sobolev-Maz’ya inequalities. Hardy inequalities and Sobolev inequalities bound the size of a function, measured by a (possibly weighted) L norm, in terms of its smoothness, measured by an integral of its gradient. Maz’ya [22] proved that for functions on the half-space R+ = {x ∈ R : xN > 0}, N ≥ 3, which vanish on the boundary, the sharp version of the Hardy inequality can be combine...
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Sharp constants are found for the trace Hardy–Sobolev inequalities in cones. The question as to whether these constants are attained is discussed. §
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2008
ISSN: 1735-8787
DOI: 10.15352/bjma/1240336296