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arXiv · 2010.10654

Improved Sobolev inequality under constraints

Fengbo Hang·Xiaodong Wang
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Abstract

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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Fengbo Hang, Xiaodong Wang. 2020-10-20. Improved Sobolev inequality under constraints. https://arxiv.org/abs/2010.10654

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