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Pré-Publication, Document De Travail Année : 2022

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

Résumé

For a smooth bounded domain $\Omega \subset \mathbb R^3$ and smooth functions $a$ and $V$, we consider the asymptotic behavior of a sequence of positive solutions $u_\epsilon$ to $-\Delta u_\epsilon + (a+\epsilon V) u_\epsilon = u_\epsilon^5$ on $\Omega$ with zero Dirichlet boundary conditions, which blow up as $\epsilon \to 0$. 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 $N=3$.

Dates et versions

hal-03869815 , version 1 (24-11-2022)

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Tobias König, Paul Laurain. Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions. 2022. ⟨hal-03869815⟩
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