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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/.

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].

On the Caffarelli-Kohn-Nirenberg

On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions † › … › 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 ...

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 ...

Minimizers of …

The Caffarelli–Kohn–Nirenberg inequalities state that there is a constant C > 0 such that

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 ...


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.


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.

On the Caffarelli–Kohn–Nirenberg

Consider the following inequalities due to Caffarelli, Kohn and Nirenberg ... We shall answer some fundamental questions concerning these inequalities ...