Singular Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field
Year: 2025
Type: article
Abstract: The first purpose of this paper is to establish the singular Trudinger–Moser inequality in R 2 ${\mathbb{R}}^{2}$ for the Aharonov–Bohm magnetic fields. The second purpose is to derive the singular Hardy–Trudinger–Moser inequality in the unit ball B 2 ${\mathbb{B}}^{2}$ with Aharonov–Bohm magnetic potential. Moreover, we will show the constant 4 π ( 1 − β 2 ) $4\pi \left(1-\frac{\beta }{2}\right)$ is sharp in these two inequalities. The main skills include providing the asymptotic estimates of the related heat kernel and adapting the level set to derive a global Trudinger–Moser inequality from a local one. These results extend the inequalities established by Lu and Yang [Calc. Var. Partial Differ. Equ., 63 (2024)] into the weighted version.
Source: Advanced Nonlinear Studies
Author: Xumin Wang
Institution: Beijing Forestry University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
Award: G2975662379
OpenAlex ID: W4409957186