Extremal functions for a singular Hardy-Moser-Trudinger inequality
Songbo Hou
TL;DR
This paper establishes a new singular Hardy-Moser-Trudinger inequality using blow-up analysis and identifies its extremal functions, extending previous results in the field.
Contribution
It introduces a novel singular Hardy-Moser-Trudinger inequality and determines the extremal functions, advancing the understanding of these inequalities.
Findings
Proved a new singular Hardy-Moser-Trudinger inequality
Identified extremal functions for the inequality
Extended previous results by Wang-Ye, Yang-Zhu, and Csató-Roy
Abstract
In this paper, using blow-up analysis, we prove a singular Hardy-Morser-Trudinger inequality, and find its extremal functions. Our results extend those of Wang-Ye (Adv. Math. 2012), Yang-Zhu ( Ann. Glob. Anal. Geom. 2016), Csat\'{o}- Roy (Calc. Var. 2015), and Yang-Zhu (J. Funct. Anal. 2017).
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Harmonic Analysis Research · Nonlinear Differential Equations Analysis