A remark on the concentration compactness principle in critical dimension

2020/02/23 by Hang, Fengbo · 1 citation
#35A23 #58C05 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.09870

Abstract

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 Aubin's theorem for functions on \mathbbSⁿ 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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