Abstract
AbstractWe prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on with zero first‐order moments of the area element to the 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. © 2020 Wiley Periodicals LLC.
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