Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality

2020/10/12 by Ao, Weiwei, DelaTorre, Azahara, Gonzalez, Maria del Mar · 1 citation
#35A23 #35C15 #35J61 #35R11 #53A30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.06004

Abstract

In this paper, we will consider the fractional Caffarelli-Kohn-Nirenberg inequality Λ (∫_{\mathbb Rⁿ}\frac|u(x)|^p|x|^β p dx)^(2)/(p)≤ ∫_{\mathbb Rⁿ}∫_{\mathbb Rⁿ}\frac(u(x)-u(y))²|x-y|^n+2γ|x|^α|y|^α dy dx where γ∈(0,1), n≥ 2, and α,β∈\mathbb R satisfy \beginequation* α≤ β≤ α+γ, -2γ

Cited by

• Fractional Sobolev logarithmic inequalities

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