On existence of minimizers for the Hardy–Sobolev–Maz’ya inequality

By A. Tertikas, Kyril Tintarev. 2005

83 citations recorded by the source corpus.

AbstractWe show existence of minimizers for the Hardy–Sobolev–Maz’ya inequality in $$\mathbb {R}^{m+n}\ \mathbb {R}^{n}$$ when either m > 2, n≥ 1 or m = 1, n≥ 3.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ef68f3a121da8f5c20a0cec90a74d01b1bd15b1a

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On the best constant of Hardy―Sobolev inequalities (2009, background): “Clearly Bn • Sn and it was shown in [ TT ] that Bn < Sn when n ‚ 4. Again, the case n = 3 turns out to be special.”
Hardy-Sobolev-Maz'ya inequalities for arbitrary domains (2011, background): “1) This inequality, its generalizations to different powers of the gradient [2] and its optimal constants [23, 3] have attracted attention recently.”
On a semilinear elliptic equation in Hn (2008, background): “[ 23 ]). Another class of equations is given by critical Grushin-type equations”
Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces (2019, unknown): “For more information about first order Hardy-Sobolev-Maz’ya in equalities, we refer to [17, 18, 19, 52, 57].”
On the structure of Hardy–Sobolev–Maz'ya inequalities (2008, unknown): “We next mention an improvement of Hardy’s inequality that involves two distance functions: ∫ R n + |∇u|2dx ≥ 1 4 ∫ R n + |u|2 x21 dx+ C(τ) ∫ R n + |u|2 x2−τ1 (x 2 1 + x 2 2) τ 2 dx, u ∈ C∞0 (Rn+), where 0 τ ≤ 1.”
A Hardy-Moser-Trudinger inequality (2010, background): “ 2, (5) Z Bn |∇u(x)|2dx− Z Bn u2 (1 −|x|2)2 dx ≥ C Z Bn |u(x)| 2n n−2dx n−2 n . Let us denote Cn the best constant such that (5) holds. In some recent works, the constant Cn has been estimated (see [28] for n > 3 and [7] for n = 3). Let Sn be the best constant for the Sobolev embedding from H1(Rn”
Hardy–Sobolev extremals, hyperbolic symmetry and scalar curvature equations (2009, unknown): “1) has been established in [6] in the special case μ = 0, k 2 and subsequently in [20] and [28] in other cases.”