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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 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 inequality on metric …

Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications Alexandru Krist´aly Department of Economics, Babe¸s-Bolyai University ...

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


THE CAFFARELLI-KOHN-NIRENBERG INEQUALITIES 877 It has been shown by Bakry, Concordet and Ledoux that (cf. [BCL]) a complete n-dimensional Riemannian ...

Caffarelli–Kohn–Nirenberg and

In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted [equation]-Sobolev type inequalities on stratified Lie groups. All ...

On the Caffarelli–Kohn–Nirenberg

We shall answer some fundamental questions concerning these inequalities such as the best embedding constants, the existence and nonexistence of extremal functions, and their qualitative properties.


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.

Horiuchi , Kumlin : On the

The main purpose of this article is to establish the Caffarelli–Kohn– Nirenberg-type (CKN-type) inequalities for all α ∈ R and to study the related matters systematically.