Differential and Integral Equations

A Paneitz-type problem in pierced domains

S. Alarcón and A. Pistoia

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 11 May 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation