Quantitative stability for the Caffarelli-Kohn-Nirenberg inequality

2023/12/25 by Zhou, Yuxuan, Zou, Wenming · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.15735

Abstract

In this paper, we investigate the following Caffarelli-Kohn-Nirenberg inequality: (∫_ℝⁿ|x|^-pa|∇ u|^pdx)^(1)/(p)≥ S(p,a,b)(∫_ℝⁿ|x|^-qb|u|^qdx)^(1)/(q), ∀ u∈ D_a^p(ℝⁿ), where S(p,a,b) is the sharp constant and a,b,p,q satisfy the relations: \beginequation* 0≤ a<(n-p)/(p), a≤ b

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