WebThere is a family of Caffarelli-Kohn-Nirenberg (CKN) inequalities which has a very similar structure. When the exponents are in a range for which the optimal functions for (CKN) … WebJan 1, 2024 · In this paper, we will apply a new representation for curl-free vector fields developed in [33] to establish a very general L 2 -CKN inequality for curl-free vector fields that contains the HUP ...
Fractional Caffarelli–Kohn–Nirenberg inequalities - Semantic Scholar
WebJul 1, 2024 · Sharp Caffarelli–Kohn–Nirenberg-Type Inequalities on Carnot Groups. J. Flynn. Mathematics. Advanced Nonlinear Studies. 2024. Abstract The main purpose of this paper is to establish several general Caffarelli–Kohn–Nirenberg (CKN) inequalities on Carnot groups G (also known as stratified groups). WebWe are interested in the Caffarelli-Kohn-Nirenberg inequality (CKN in short), introduced by these authors in 1984. We explain why the CKN inequality can be viewed as a Sobolev … cut photos for instagram feed
A Note About a Caffarelli–Kohn–Nirenberg Type Inequality
WebOct 1, 2024 · Sharp. L. 2. -Caffarelli–Kohn–Nirenberg inequalities for Grushin vector fields. 1. Introduction. It was observed by Costa in [5] that the L 2 -Caffarelli–Kohn–Nirenberg (CKN) inequalities [2] on R N may be obtained by the elementary fact that A s 2 + B s + C ≥ 0 holding for all s ∈ R implies B 2 − 4 A C ≤ 0. WebThe fractional CKN inequality Consider 2(0;1), n >2, and ; 2R satisfy + ; 2 < < n 2 2; and p = 2n n 2 + 2( ): The fractional Ca arelli-Kohn-Nirenberg inequality is Z R n ju(x)jp jxj p dx 2 p R R (u(x) u(y))2 jx yjn+2 jxj jyj dy dx (FCKN) Known results by Abdellaoui and Bentifour, Musina and Nazarou, Nguyen and Squassina WebMar 23, 2024 · In this paper, we prove one Caffarelli–Kohn–Nirenberg type (CKN) inequality for submanifolds into the Euclidean space using a direct but very efficient approach. We notice that the analysis of the zeros of the weight function on the submanifold was done in the proof of Hardy-type inequality in Theorem 3.1 and thus we pass … cut photoshop