Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909628496871424 |
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| author | Pistoia, Angela Rago, Giuseppe Mario Vaira, Giusi |
| author_facet | Pistoia, Angela Rago, Giuseppe Mario Vaira, Giusi |
| contents | The paper addresses the existence of multi-bubble solutions for the well-known Brezis-Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded domain remains an open problem. The goal of the present paper is to resolve this longstanding issue. In particular, we exhibit examples of domains where a large number of multi-bubble solutions exist. Our result can also be seen as the counterpart of the asymptotic analysis carried out by Konig and Laurin in Ann. Inst. H. Poincarè C Anal. Non Linèaire, 2024. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions Pistoia, Angela Rago, Giuseppe Mario Vaira, Giusi Analysis of PDEs 35B44, 35B33, 35J25 The paper addresses the existence of multi-bubble solutions for the well-known Brezis-Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded domain remains an open problem. The goal of the present paper is to resolve this longstanding issue. In particular, we exhibit examples of domains where a large number of multi-bubble solutions exist. Our result can also be seen as the counterpart of the asymptotic analysis carried out by Konig and Laurin in Ann. Inst. H. Poincarè C Anal. Non Linèaire, 2024. |
| title | Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions |
| topic | Analysis of PDEs 35B44, 35B33, 35J25 |
| url | https://arxiv.org/abs/2505.24387 |