On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem

2017/03/17 by Nguyen, Van Hoang, Takahashi, Futoshi
#26D10 #35A23 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.05934

Abstract

In this paper, we establish a weighted Trudinger-Moser type inequality with the full Sobolev norm constraint on the whole Euclidean space. Main tool is the singular Trudinger-Moser inequality on the whole space recently established by Adimurthi and Yang, and a transformation of functions. We also discuss the existence and non-existence of maximizers for the associated variational problem.

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