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arXiv · 1307.4067

A Paneitz-type problem in pierced domains

S. Alarcón·A. Pistoia
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Abstract

We study the critical problem {equation} {{array}{ll} Δ^{2}u=u^{\frac{N+4}{N-4}} & {in}Ω\setminus \bar{B(ξ_0,\varepsilon)},\medskip u>0&{in}Ω\setminus \bar{B(ξ_0,\varepsilon)},\medskip u=Δu=0 & {on}\partial (Ω\setminus \bar{B(ξ_0,\varepsilon)}),{array}. \tag{P$_\varepsilon$} {equation} where $Ω$ is an open bounded domain in $\mathbb{R}^N$, $N\ge5$, $ξ_0\inΩ$ and $B(ξ_0,\varepsilon)$ is the ball centered at $ξ_0$ with radius $\varepsilon>0$ small enough. We construct solutions of (P$_\varepsilon$) blowing-up at the center of the hole as the size of the hole goes to zero.

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S. Alarcón, A. Pistoia. 2013-07-15. A Paneitz-type problem in pierced domains. https://arxiv.org/abs/1307.4067

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