Extremals for the singular Moser-Trudinger inequality via n-harmonic transplantation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:270

Article

Csato, Gyula^1,2  Van Hoang Nguyen^3,4  Roy, Prosenjit⁵ 

[1] Univ Barcelona, Barcelona, Spain

[2] BGSMath Barcelona, Barcelona, Spain

[3] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam

[4] FPT Univ, Dept Math, Hanoi, Vietnam

[5] Indian Inst Technol, Kanpur, Uttar Pradesh, India

关键词: Moser Trudinger inequality;    Extremal function;   

DOI  :  10.1016/j.jde.2020.08.005

来源: Elsevier

【 摘 要 】

The Moser-Trudinger embedding has been generalized in Adimurthi and Sandeep (2007) [2] to the following weighted version: if Omega subset of R-n is bounded, omega(n-1) is the Hn-1 measure of the unit sphere, then for alpha > 0 and beta is an element of [0, n), sub (u is an element of B1) integral(Omega )e(alpha vertical bar u vertical bar n/(n-1))/vertical bar x vertical bar(beta) <= C double left right arrow alpha/alpha(n) + beta/n <= 1, where alpha(n) = n omega(1/(n-1))(n-1) and B-1 = { u is an element of W-0(1)'(n) (Omega) vertical bar integral(Omega) vertical bar vertical bar del u vertical bar(n) <= 1}. We prove that the supremum is attained on any domain Omega. The paper also fills in the gaps in the proof of Lin (1996) [21], which deals with the case beta = 0. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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