September 16, 2025

Existence of minimizers of the stability constant of Caffarelli–Kohn–Nirenberg inequality

Key Points

Minimizers exist for the sharp stability constant of the Caffarelli–Kohn–Nirenberg inequality.
An upper bound is provided with an explicit sharp constant, extending prior work in this area.
The results build upon existing literature while indicating potential areas for further research.
The new curve $b^*_{ ext{FS}}(a)$ offers insights into the stability of the inequality.

Abstract

Abstract In this paper, we prove the existence of minimizers for the sharp stability constant of Caffarelli–Kohn–Nirenberg inequality near the new curve b^*₅ₒ (a) (which lies above the well-known Felli–Schneider curve b₅ₒ (a) ), extending the work of Wei and Wu Math. Z. , 2024 to a slightly larger region. Moreover, we provide an upper bound for the Caffarelli–Kohn–Nirenberg inequality with an explicit sharp constant, which may have its own interest.

Existence of minimizers of the stability constant of Caffarelli–Kohn–Nirenberg inequality

Key Points

Abstract

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