Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929494548283392 |
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| author | Malizia, Francesco |
| author_facet | Malizia, Francesco |
| contents | We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field equations in a supercritical regime. Moreover, we also discuss an extension of this result to the case of singular Liouville equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional Malizia, Francesco Analysis of PDEs 35B44, 35J61, 35R01, 49J35 We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field equations in a supercritical regime. Moreover, we also discuss an extension of this result to the case of singular Liouville equations. |
| title | Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional |
| topic | Analysis of PDEs 35B44, 35J61, 35R01, 49J35 |
| url | https://arxiv.org/abs/2409.06515 |