The effect of curvature in fractional Hardy--Sobolev inequality with the Spectral Dirichlet Laplacian

2019/06/18 by Nikita Ustinov, Ustinov, Nikita
Mathematics · #35B45 #35R11 #49J10 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1906.07519

openalex publication_date 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the attainability of the best constant in the fractional Hardy--Sobolev inequality with boundary singularity for the Spectral Dirichlet Laplacian. The main assumption is the average concavity of the boundary at the origin.

Citations

• The Pohozaev Identity for the Fractional Laplacian

Related

• Attainability of the best constant of Hardy-Sobolev inequality with full boundary singularities
• Fractional Hardy-Sobolev inequalities on half spaces
• The Effect of Curvature on the Best Constatnt in the Hardy-Sobolev Inequalities
• The role of the mean curvature in a Hardy-Sobolev trace inequality
• The best constant in a fractional Hardy inequality