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On the Caffarelli-Kohn-Nirenberg Inequalities

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On the Caffarelli-Kohn-Nirenberg Inequalities: Sharp ...

CAFFARELLI-KOHN-NIRENBERG INEQUALITIES 233 equation corresponding to (1.8). The two problems will be shown to be equivalent, and we shall mainly work on the transformed one on R SN−1. The advantage in working on the latter is that the equation is an autonomous one and is defined in H1.R SN−1/.
http://www.math.usu.edu/~wang/cpam.pdf

On the Caffarelli-Kohn-Nirenberg

We consider positive solutions of -div(|x|-2a u) = |x|-bpup-1, u ≥ 0 in RN, where for N ≥ 2: a < (N - 2)/2, a < b < a + 1, and p = 2N/(N - 2(1 + a - b)). Ground state solutions are the extremal functions of the Caffarelli-Kohn-Nirenberg inequalities [6].
https://www.researchgate.net/publication/2452776_On_the_Caffarelli...

On the Caffarelli-Kohn-Nirenberg

On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions †
http://onlinelibrary.wiley.com › … › Vol 54 Issue 2 › Abstract

On the Caffarelli–Kohn–Nirenberg inequalities

C. R. Acad. Sci. Paris, t. 330, Série I, p. 437–442, 2000 Équations aux dérivées partielles/Partial Differential Equations On the Caffarelli–Kohn ...
http://math.usu.edu/~wang/CRAS-2000.pdf

Caffarelli-Kohn-Nirenberg inequalities

In the setting of a Lie group of polynomial volume growth, we derive inequalities of Caffarelli-Kohn-Nirenberg type, where the weights involved are powers ...
https://www.researchgate.net/publication/313797480_Caffarelli-Kohn...

Minimizers of …

The Caffarelli–Kohn–Nirenberg inequalities state that there is a constant C > 0 such that
https://link.springer.com/article/10.1007/s00205-009-0269-y

On Caffarelli–Kohn–Nirenberg-type

We investigate Caffarelli–Kohn–Nirenberg-type inequalities for the weighted biharmonic operator in cones, both under Navier and Dirichlet boundary ...
https://link.springer.com/article/10.1007/s00032-011-0167-2

CAFFARELLI-KOHN-NIRENBERG INEQUALITIES

inequalities (i.e., 0 < a < 1 and at least one of s,µ,θ is nonzero), see the review paper by Dolbeault and Esteban [15]. Compared with the special cases of the Gagliardo-Nirenberg inequalities without the interpolation term (i.e., a = 1), dealing with such CKN inequalities encounters considerably more difficulty.
https://arxiv.org/pdf/1510.01224.pdf

THE CAFFARELLI-KOHN-NIRENBERG INEQUALITIES ON

Another important inequality is the so called Nash inequality stating that for any f ∈ C∞ 0 (IRn) we have Z IRn f2dv 1+2/n ≤ C n IRn |∇f|2dv Z IRn |f|dv 4/n (1.8) for a constant C n depending only on n. This inequality is a particular case of the Gagliardo-Nirenberg inequalities for which numerous applications have been found.
http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2007/0014/0005/...

On the Caffarelli–Kohn–Nirenberg

Consider the following inequalities due to Caffarelli, Kohn and Nirenberg ... We shall answer some fundamental questions concerning these inequalities ...
https://www.sciencedirect.com/science/article/pii/S0764444200002019