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arXiv · 2208.12337

Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions

Tobias König·Paul Laurain
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Abstract

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 $N=3$.

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Tobias König, Paul Laurain. 2025-12-20. Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions. https://arxiv.org/abs/2208.12337

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