论文标题
log-sobolev和Moser-onofri不平等的急剧稳定性
Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere
论文作者
论文摘要
在本文中，我们关注的是Sobolev不平等的端点不变案例的稳定性问题，$ \ Mathbb {s}^n $。也就是说，我们将确立贝克纳的log-sobolev不平等现象和贝克纳的Moser-onofri不平等现象的稳定性。我们还证明，log-sobolev不等式的全球稳定性的急剧常数$ \ mathbb {s}^n $必须严格小于同一不平等的局部稳定性的急剧稳定性。此外，我们还得出了Moser-Onofri不平等的全局稳定性的不存在，$ \ mathbb {s}^n $。
In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere $\mathbb{S}^n$. Namely, we will establish the stability for Beckner's log-Sobolev inequality and Beckner's Moser-Onofri inequality on the sphere. We also prove that the sharp constant of global stability for the log-Sobolev inequality on the sphere $\mathbb{S}^n$ must be strictly smaller than the sharp constant of local stability for the same inequality. Furthermore, we also derive the non-existence of the global stability for Moser-Onofri inequality on the sphere $\mathbb{S}^n$.
