约束下改进的Sobolev不等式

arXiv: Classical Analysis and ODEs Pub Date : 2020-10-20 DOI:10.1093/IMRN/RNAB067

Fengbo Hang, Xiaodong Wang

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引用次数: 6

摘要

在$\mathbb{S}^{n}$上给出了Aubin对Sobolev不等式的改进，在面积元的一阶矩消失的情况下给出了新的证明，并将其推广到高阶矩的情况。通过对$\mathbb{S}^{n}$上的一个极值问题的仔细研究，我们明确地确定了二阶矩情况下的常数。

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Improved Sobolev Inequality Under Constraints

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.

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来源期刊

arXiv: Classical Analysis and ODEs

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