【摘要】Inthispaper,weprovethat,if0<k<l,2k=n,ΩR~n,u∈H~l(Ω),theSobolevinequalityholdsinlimitingcases:LetWeconsiderthefollowingproblem:-△U_ρ~s(X)=W_ρ~s(x-b)inΩ,u_ρ~s(x)=0onΓ.Letu_ρ(s)=maxx∈Ωu_ρ~s(x).By(1),ifsisincreasing,thegradualchangeofW_ρ~s(x-b)givesrisetothesuddenchangeofuρ(s).Thissuddenchangeo
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