On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem. (English) Zbl 1463.35026

Nguyen, Van Hoang; Takahashi, Futoshi

Differ. Integral Equ. 31, No. 11-12, 785-806 (2018).

Summary: 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 Y. Yang [Int. Math. Res. Not. 2010, No. 13, 2394–2426 (2010; Zbl 1198.35012)], and a transformation of functions. We also discuss the existence and non-existence of maximizers for the associated variational problem.

MSC:

35A23	Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

Trudinger-Moser inequality; weighted Sobolev spaces; maximizing problem; attainability

Citations:

Zbl 1198.35012