典型文献
Critical Trace Trudinger-Moser Inequalities on a Compact Riemann Surface with Smooth Boundary
文献摘要：
In this paper,the author concerns two trace Trudinger-Moser inequalities and obtains the corresponding extremal functions on a compact Riemann surface(∑,g)with smooth boundary ?Σ.Explicitly,letλ1( ?∑) infu∈W1,2（Σ，g），∫?Σudsg=0,u(≠)0∫Σ（|▽gu|2+u2)dvg/∫aΣu2dsg and H={u∈W1,2(∑, g) : ∫∑ (|▽gu|2+u2)dvg - α∫?∑u2dsg ≤ 1 and ∫?∑udsg=0}, where W1,2(∑, g) denotes the usual Sobolev space and ▽g stands for the gradient operator.By the method of blow-up analysis, we obtain supu∈H∫?∑ eπu2dsg dsg{＜+∞,0≤α＜λ1(?∑),=+∞ α＞λ1(?∑).Moreover, the author proves the above supremum is attained by a function uα € H∩C∞ (∑)for any 0 ＜ α ＜ λ1(?Σ). Further, he extends the result to the case of higher order eigenvalues. The results generalize those of [Li, Y. and Liu, P., Moser-Trudinger inequality on the boundary of compact Riemannian surface, Math. Z., 250, 2005, 363-386], [Yang, Y., Moser-Trudinger trace inequalities on a compact Riemannian surface with boundary, Pacific J. Math., 227, 2006, 177-200] and [Yang, Y., Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two, J. Diff. Eq., 258, 2015,3161-3193].
文献关键词：
中图分类号：
作者姓名：
Mengjie ZHANG
作者机构：
School of Mathematics,Renmin University of China,Beijing 100872,China
文献出处：
引用格式：
[1]Mengjie ZHANG-.Critical Trace Trudinger-Moser Inequalities on a Compact Riemann Surface with Smooth Boundary)[J].数学年刊B辑（英文版）,2022(03):425-442
A类：
infu,udsg,2+u2,dvg,u2dsg,supu,dsg,Extremal,Adimurthi,Druet
B类：
Critical,Trace,Trudinger,Moser,Inequalities,Compact,Surface,Smooth,Boundary,this,paper,author,concerns,two,trace,inequalities,obtains,corresponding,extremal,functions,compact,surface,smooth,boundary,Explicitly,let,W1,gu,where,denotes,usual,Sobolev,space,stands,gradient,operator,By,method,blow,analysis,we,Moreover,proves,above,supremum,attained,by,any,Further,extends,case,higher,order,eigenvalues,results,generalize,those,Liu,inequality,Riemannian,Math,Yang,Pacific,type,dimension,Diff,Eq
AB值：
0.462356
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