Concentration-Compactness principle for the sharp Adams inequalities in bounded domains and whole space Rn

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Van Hoang Nguyen¹ 

[1] Duy Tan Univ, Inst Res & Dev, Da Nang, Vietnam

关键词: Moser-Trudinger inequality;    Adams inequality;    Lions Concentration-Compactness principle;    Decreasing rearrangement;    Best constant;    Sobolev spaces;   

DOI  :  10.1016/j.jde.2019.05.010

来源: Elsevier

【 摘 要 】

We prove an improvement of the sharp Adams inequality in W-0(m, n/m)(Omega) where Omega is a bounded domain in R-n inspired by Lions Concentration-Compactness principle for the sharp Moser-Trudinger inequality. Our method gives an alternative approach to a Concentration-Compactness principle in W-0(m, n/m)(Omega) recently established by do O and Macedo. Furthermore, we obtain a sharp threshold for m odd improving the one of do O and Macedo. Our approach is also successfully applied to whole space R-n to establish the improvements of the sharp Adams inequalities in W-m,W- n/m(R-n). This type of improvement is still unknown, in general, except the case m = 1 due to do O, de Souza, de Medeiros and Severo. Our method is a further development of the one of Cerny, Cianchi and Hencl combining with some estimates for the decreasing rearrangement of a function in terms of the one of its higher order derivatives. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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