A singular Adams' inequality with logarithmic weights and applications

Abstract

In this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of ${\mathbb{R}}^4$. Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in ${\mathbb{R}}^4$. Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established.

Keywords:

• Singular Adams' inequality
• logarithmic weights
• weighted mean field equations

2010 Mathematics Subject Classifications:

• 35A21
• 35A23
• 35D30
• 35J25

Disclosure statement

No potential conflict of interest was reported by the author(s).