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A remark on the concentration compactness principle in critical dimension

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 نشر من قبل Fengbo Hang
 تاريخ النشر 2020
  مجال البحث
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 تأليف Fengbo Hang




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We prove some refinements of concentration compactness principle for Sobolev space $W^{1,n}$ on a smooth compact Riemannian manifold of dimension $n$. As an application, we extend Aubins theorem for functions on $mathbb{S}^{n}$ with zero first order moments of the area element to higher order moments case. Our arguments are very flexible and can be easily modified for functions satisfying various boundary conditions or belonging to higher order Sobolev spaces.



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