Extremal Functions for Trudinger-Moser Type Inequalities in IRN

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Extremal function Trudinger-Moser inequality
• 年，卷（期）: 2017,（1）
• 页码范围: 64-75
• 页数: 12页
• 分类号: O175.29
• 语种: 英文
• DOI: 10.4208/jpde.v30.n1.5

摘要

Let N≥ 2,αN =NωN 1/(N-1)N-1,where ωN-1 denotes the area of the unit sphere in IRN.In this note,we prove that for any 0 ＜ α ＜ αN and anyβ ＞ 0,the supremum u∈W1,N(IRN),sup||u||W1,N(IRN)≤1∫IRN|u|β(eα|u|N/N-1-N-2Σj=0αj/j!|u|Nj/N-1)dxcan be attained by some function u ∈ W1'N (RN) with || u|| w1,N (IRN) =1.Moreover,when α ≥ αN,the above supremum is infinity.