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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.14306 |
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| _version_ | 1866909996428558336 |
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| author | Wu, Lina Zou, Wenming |
| author_facet | Wu, Lina Zou, Wenming |
| contents | For a regular mean field equation defined on a compact Riemann surface, an important work of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4} proved a uniqueness theorem for blow-up solutions under non-degeneracy assumptions. However, the proof is highly nontrivial and challenging to read. In this article, we not only provide a simple proof for the regular equation but also extend our proof to the case of singular equations with negative singular poles. Our proof supplements what is not written in a recent outstanding work by Bartolucci-Yang-Zhang \cite{byz-1}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A simple proof of the Uniqueness of blow-up solutions of mean field equations Wu, Lina Zou, Wenming Analysis of PDEs For a regular mean field equation defined on a compact Riemann surface, an important work of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4} proved a uniqueness theorem for blow-up solutions under non-degeneracy assumptions. However, the proof is highly nontrivial and challenging to read. In this article, we not only provide a simple proof for the regular equation but also extend our proof to the case of singular equations with negative singular poles. Our proof supplements what is not written in a recent outstanding work by Bartolucci-Yang-Zhang \cite{byz-1}. |
| title | A simple proof of the Uniqueness of blow-up solutions of mean field equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.14306 |