Singular Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field
The first purpose of this paper is to establish the singular Trudinger–Moser inequality in R2 ${\mathbb{R}}^{2}$ for the Aharonov–Bohm magnetic fields. The second purpose is to derive the singular Hardy–Trudinger–Moser inequality in the unit ball B2 ${\mathbb{B}}^{2}$ with Aharonov–Bohm magnetic p...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-04-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0187 |
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| Summary: | The first purpose of this paper is to establish the singular Trudinger–Moser inequality in R2
${\mathbb{R}}^{2}$
for the Aharonov–Bohm magnetic fields. The second purpose is to derive the singular Hardy–Trudinger–Moser inequality in the unit ball B2
${\mathbb{B}}^{2}$
with Aharonov–Bohm magnetic potential. Moreover, we will show the constant 4π(1−β2)
$4\pi \left(1-\frac{\beta }{2}\right)$
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. |
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| ISSN: | 2169-0375 |