Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities

2024/08/14 by Haixia Chen, Chen, Haixia, Seunghyeok Kim +3 · 3 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2408.07775

openalex publication_date 2024/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding H^s(\mathbb Rⁿ) \hookrightarrow L^{2n \over n-2s}(\mathbb Rⁿ) in the whole range of s ∈ (0,(n)/(2)).

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