Role of the fundamental solution in Hardy—Sobolev-type inequalities
2006 ◽
Vol 136
(6)
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pp. 1111-1130
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Keyword(s):
Let n ≥ 3, Ω ⊂ Rn be a domain with 0 ∈ Ω, then, for all the Hardy–Sobolev inequality says that and equality holds if and only if u = 0 and ((n − 2)/2)2 is the best constant which is never achieved. In view of this, there is scope for improving this inequality further. In this paper we have investigated this problem by using the fundamental solutions and have obtained the optimal estimates. Furthermore, we have shown that this technique is used to obtain the Hardy–Sobolev type inequalities on manifolds and also on the Heisenberg group.
2006 ◽
Vol 136
(2)
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pp. 277-300
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1997 ◽
Vol 49
(6)
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pp. 1299-1322
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1978 ◽
Vol 36
(1)
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pp. 176-177
Keyword(s):
1986 ◽
Vol 29
(1)
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pp. 47-56
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Keyword(s):
2003 ◽
pp. 757-765
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2019 ◽
Vol 35
(7)
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pp. 720-731
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Keyword(s):
1938 ◽
Vol 34
(3)
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pp. 316-320
Keyword(s):