On Non-simple blowup solutions of Liouville equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909454628290560 |
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| author | D'Aprile, Teresa Wei, Juncheng Zhang, Lei |
| author_facet | D'Aprile, Teresa Wei, Juncheng Zhang, Lei |
| contents | For Liouville equation with quantized singular sources, the non-simple blowup phenomenon has been a major difficulty for years. It was conjectured by the first two authors that the non-simple blowup phenomenon does not occur if the equation is defined on the unit ball with Dirichlet boundary condition. In this article we not only completely settle this conjecture in its entirety, but also extend our result to cover any bounded domain. Since the main theorem in this article rules out the non-simple phenomenon in commonly observed applications, it may pave the way for advances in degree counting programs, uniqueness of blowup solutions and construction of solutions, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05271 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Non-simple blowup solutions of Liouville equation D'Aprile, Teresa Wei, Juncheng Zhang, Lei Analysis of PDEs 35J75, 35J61 For Liouville equation with quantized singular sources, the non-simple blowup phenomenon has been a major difficulty for years. It was conjectured by the first two authors that the non-simple blowup phenomenon does not occur if the equation is defined on the unit ball with Dirichlet boundary condition. In this article we not only completely settle this conjecture in its entirety, but also extend our result to cover any bounded domain. Since the main theorem in this article rules out the non-simple phenomenon in commonly observed applications, it may pave the way for advances in degree counting programs, uniqueness of blowup solutions and construction of solutions, etc. |
| title | On Non-simple blowup solutions of Liouville equation |
| topic | Analysis of PDEs 35J75, 35J61 |
| url | https://arxiv.org/abs/2209.05271 |