Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 31, Issue 2, Pages 297-314Publisher
ELSEVIER
DOI: 10.1016/j.anihpc.2013.03.004
Keywords
Weighted Trudinger-Moser inequality; Existence of maximizer; Caffarelli-Kohn-Nirenberg inequality with asymptotics
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Funding
- Grants-in-Aid for Scientific Research [23340038, 26247014, 26610030] Funding Source: KAKEN
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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. (C) 2013 Elsevier Masson SAS. All rights reserved.
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