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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00036 |
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| _version_ | 1866909275203305472 |
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| author | Wu, Lina |
| author_facet | Wu, Lina |
| contents | In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complementary result on a singular mean field equation with a sign-changing potential function Wu, Lina Analysis of PDEs In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold. |
| title | A complementary result on a singular mean field equation with a sign-changing potential function |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.00036 |