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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.12337 |
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| _version_ | 1866909971249102848 |
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| author | König, Tobias Laurain, Paul |
| author_facet | König, Tobias Laurain, Paul |
| contents | For a smooth bounded domain $Ω\subset \mathbb R^3$ and smooth functions $a$ and $V$, we consider the asymptotic behavior of a sequence of positive solutions $u_ε$ to $-Δu_ε+ (a+εV) u_ε= u_ε^5$ on $Ω$ with zero Dirichlet boundary conditions, which blow up as $ε\to 0$. We derive the sharp blow-up rate and characterize the location of concentration points in the general case of multiple blow-up, thereby obtaining a complete picture of blow-up phenomena in the framework of the Brezis-Peletier conjecture in dimension $N=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12337 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions König, Tobias Laurain, Paul Analysis of PDEs For a smooth bounded domain $Ω\subset \mathbb R^3$ and smooth functions $a$ and $V$, we consider the asymptotic behavior of a sequence of positive solutions $u_ε$ to $-Δu_ε+ (a+εV) u_ε= u_ε^5$ on $Ω$ with zero Dirichlet boundary conditions, which blow up as $ε\to 0$. We derive the sharp blow-up rate and characterize the location of concentration points in the general case of multiple blow-up, thereby obtaining a complete picture of blow-up phenomena in the framework of the Brezis-Peletier conjecture in dimension $N=3$. |
| title | Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2208.12337 |