This paper proves minimizers exist for the stability constant of the Caffarelli–Kohn–Nirenberg inequality, suggesting new bounds.
In this paper, we prove the existence of minimizers for the sharp stability constant of Caffarelli–Kohn–Nirenberg inequality near the new curve b^*FS(a) (which lies above the well-known Felli–Schneider curve bFS(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.
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Deng et al. (2025) studied this question.