摘要
Let W^(1,n)(R^(n))be the standard Sobolev space.For any T>0 and p>n>2,we denote■Define a norm in W^(1,n)(R^(n))by■where 0≤α<λ_(n,p).Using a rearrangement argument and blow-up analysis,we will prove■can be attained by some function u_(0)∈W^(1,n)(R^(n))∩C^(1)(R^(n))with ||u_(0)||_(n,p)=1,here a_(n)=n■_(n-1)^(1/n-1) and ■_(n-1) is the measure of the unit sphere in R^(n).
基金
supported by National Science Foundation of China(Grant No.12201234)
Natural Science Foundation of Anhui Province of China(Grant No.2008085MA07)
the Natural Science Foundation of the Education Department of Anhui Province(Grant No.KJ2020A1198).
