Trudinger type inequalities in RN and their best exponents

被引：312

作者：

Adachi, S ^{[1
]}

Tanaka, K ^{[1
]}

机构：

[1] Waseda Univ, Sch Sci & Engn, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 07期

关键词：

D O I：

10.1090/S0002-9939-99-05180-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Trudinger type inequalities in R-N and their best exponents alpha(N). We show for alpha is an element of (0, alpha(N)), alpha(N) = N omega(N-1)((N-1)) (omega(N-1) is the surface area of the unit sphere in R-N), there exists a constant C-alpha>0 such that [GRAPHICS] for all u is an element of W-1,W-N (R-N) \ {0}. Here Phi(N) (xi) is defined by [GRAPHICS] is also shown that (*) with alpha greater than or equal to alpha(N) is false, which is different from the usual Trudinger's inequalities in bounded domains.

引用

页码：2051 / 2057

页数：7

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