On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form
On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form
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DOI：
10.1016/j.anihpc.2013.03.004
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发表时间：
2014-03
影响因子：
1.9
通讯作者：
M. Ishiwata;Makoto Nakamura;H. Wadade
中科院分区：
文献类型：
--
作者：
M. Ishiwata;Makoto Nakamura;H. Wadade
In this article, we establish the weighted Trudinger–Moser inequality of the scaling invariant form including its best constant and prove the existence of a maximizer for the associated variational problem. The non-singular case was treated by Adachi and Tanaka (1999)[1] and the existence of a maximizer is a new result even for the non-singular case. We also discuss the relation between the best constants of the weighted Trudinger–Moser inequality and the Caffarelli–Kohn–Nirenberg inequality in the asymptotic sense.© 2013 Elsevier Masson SAS. All rights reserved.
