论文标题
改善了约束的Sobolev不平等
Improved Sobolev inequality under constraints
论文作者
论文摘要
我们给出了奥本在$ \ mathbb {s}^{n} $上改善sobolev不平等的新证明，在该区域元素的一阶矩消失下，并将其推广到更高阶段的情况下。通过仔细研究$ \ mathbb {s}^{n} $上的极端问题，我们在第二阶矩情况下明确确定了常数。
We give a new proof of Aubin's improvement of the Sobolev inequality on $\mathbb{S}^{n}$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on $\mathbb{S}^{n}$, we determine the constant explicitly in the second order moments case.
