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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12057 |
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| _version_ | 1866929656254431232 |
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| author | Bartolucci, Daniele Yang, Wen Zhang, Lei |
| author_facet | Bartolucci, Daniele Yang, Wen Zhang, Lei |
| contents | For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result covers the most general case extending or improving all previous works of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4,bart-4-2} and Wu-Zhang \cite{wu-zhang-ccm}. For example, unlike previous results, we drop the assumption of singular sources being critical points of a suitably defined Kirchoff-Routh type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular we come up with several new estimates of independent interest about the concentration phenomenon for Liouville-type equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations Bartolucci, Daniele Yang, Wen Zhang, Lei Analysis of PDEs 35J60, 53C21 For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result covers the most general case extending or improving all previous works of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4,bart-4-2} and Wu-Zhang \cite{wu-zhang-ccm}. For example, unlike previous results, we drop the assumption of singular sources being critical points of a suitably defined Kirchoff-Routh type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular we come up with several new estimates of independent interest about the concentration phenomenon for Liouville-type equations. |
| title | Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations |
| topic | Analysis of PDEs 35J60, 53C21 |
| url | https://arxiv.org/abs/2401.12057 |