Existence of extremals for stability of nonlocal Sobolev inequality
Abstract
Abstract This paper is devoted to quantitative refinements of the nonlocal Sobolev inequality with explicit determination of stability constants. In the single-bubble regime, we rigorously prove that the optimal stability constant c HLS = inf u ∈ D 1,2 ( R N ) \ M ‖ ∇ u ‖ L 2 ( R N ) 2 − S HLS ∫ R N I μ ∗ | u | 2 μ * | u | 2 μ * d x 1 2 μ *
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Mathematical Inequalities and Applications
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Advanced Nonlinear Studies
- Volume
- 26
- Issue
- 1
- Pages
- 274–297
- Publication date
- 27 January 2026
- Language
- EN