Differential and Integral Equations

A Paneitz-type problem in pierced domains

S. Alarcón and A. Pistoia

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Abstract

We study the critical problem \begin{equation} \left\{ \begin{array}{ll} \Delta ^{2}u=u^{\frac{N+4}{N-4} } & \mbox{ in }\Omega\setminus \overline{B(\xi_0,\varepsilon) }, \\ u>0 & \mbox{ in }\Omega\setminus \overline{B(\xi_0,\varepsilon) }, \\ u=\Delta u=0 & \mbox{ on }\partial (\Omega \setminus \overline{B(\xi_0,\varepsilon) }), \end{array} \right. \tag{P$_\varepsilon$} \end{equation} where $\Omega$ is an open bounded domain in $\mathbb{R}^N$, $N\ge5$, $\xi_0\in\Omega$ and $B(\xi_0,\varepsilon)$ is the ball centered at $\xi_0$ 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.

Article information

Source
Differential Integral Equations, Volume 28, Number 7/8 (2015), 823-838.

Dates
First available in Project Euclid: 11 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1431347865

Mathematical Reviews number (MathSciNet)
MR3345335

Zentralblatt MATH identifier
1363.35103

Subjects
Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35B25: Singular perturbations 35J35: Variational methods for higher-order elliptic equations 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian

Citation

Alarcón, S.; Pistoia, A. A Paneitz-type problem in pierced domains. Differential Integral Equations 28 (2015), no. 7/8, 823--838. https://projecteuclid.org/euclid.die/1431347865


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