Critical Hardy–Sobolev inequalities
By Stathis Filippas, V. Maz’ya, A. Tertikas. 2006
113 citations recorded by the source corpus.
Abstract We consider Hardy inequalities in R n , n ⩾ 3 , with best constant that involve either distance to the boundary or distance to a surface of co-dimension k n , and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/d814e9f8b9309702f2770503d58a55e837cb09e3
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- On the structure of Hardy–Sobolev–Maz'ya inequalities (2008, background): “For results in the critical case we refer to [8].”
- A geometric characterization of a sharp Hardy inequality (2011, methodology): “4 in [17], we can extend the HardySobolev inequality to weakly mean convex domains.”
- Hardy-Sobolev-Maz'ya inequalities for arbitrary domains (2011, background): “mains [21], since by the same argument leading to (1.4) one sees that DΩ,p(x) ≤ dist(x,Ωc) if Ω is convex. (1.10) Hardy-Sobolev inequalities for p>2 and smooth, convex domains were also studied in [10]. The following theorem extends this to arbitrary domains. Theorem 1.3. Let 2 ≤ p<N. There is”
- Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, background): “in the interpolation term. There are great efforts to investigate the sharp constants, existence/nonexistence and symmetry/symmetry breaking of maximizers in this situation, especially when p = 2. See [6, 9, 11, 14, 25, 38], among others. For instance, Chou and Chu considered the case p = 2 and µ 2 ≤”