Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions

Fuente: arXiv
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Hauptverfasser: Pistoia, Angela, Rago, Giuseppe Mario, Vaira, Giusi
Format: Preprint
Veröffentlicht: 2025
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_version_ 1866909628496871424
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