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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/2409.04664 |
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| _version_ | 1866910773046935552 |
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| author | Bartolucci, Daniele Yang, Wen Zhang, Lei |
| author_facet | Bartolucci, Daniele Yang, Wen Zhang, Lei |
| contents | We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This extends the results from Bartolucci-Jevnikar-Lee-Yang \cite{bart-5}, which focused on regular blow-up points. As a consequence, we establish the strict convexity of the Entropy in the large energy limit for a specific class of two-dimensional domains in the Onsager mean field vortex model with singular sources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non degeneracy of blow-up solutions of non-quantized singular Liouville-type equations and the convexity of the mean field entropy of the Onsager vortex model with singular sources Bartolucci, Daniele Yang, Wen Zhang, Lei Analysis of PDEs Mathematical Physics 35J60, 82C40, 53C21 We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This extends the results from Bartolucci-Jevnikar-Lee-Yang \cite{bart-5}, which focused on regular blow-up points. As a consequence, we establish the strict convexity of the Entropy in the large energy limit for a specific class of two-dimensional domains in the Onsager mean field vortex model with singular sources. |
| title | Non degeneracy of blow-up solutions of non-quantized singular Liouville-type equations and the convexity of the mean field entropy of the Onsager vortex model with singular sources |
| topic | Analysis of PDEs Mathematical Physics 35J60, 82C40, 53C21 |
| url | https://arxiv.org/abs/2409.04664 |