Differential and Integral Equations

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

Van Hoang Nguyen and Futoshi Takahashi

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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.

Article information

Source
Differential Integral Equations, Volume 31, Number 11/12 (2018), 785-806.

Dates
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1537840869

Mathematical Reviews number (MathSciNet)
MR3857864

Zentralblatt MATH identifier
06986978

Subjects
Primary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals 26D10: Inequalities involving derivatives and differential and integral operators

Citation

Nguyen, Van Hoang; Takahashi, Futoshi. On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem. Differential Integral Equations 31 (2018), no. 11/12, 785--806. https://projecteuclid.org/euclid.die/1537840869


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