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July/August 2015 A Paneitz-type problem in pierced domains
S. Alarcón, A. Pistoia
Differential Integral Equations 28(7/8): 823-838 (July/August 2015).

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.

Citation

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S. Alarcón. A. Pistoia. "A Paneitz-type problem in pierced domains." Differential Integral Equations 28 (7/8) 823 - 838, July/August 2015.

Information

Published: July/August 2015
First available in Project Euclid: 11 May 2015

zbMATH: 1363.35103
MathSciNet: MR3345335

Subjects:
Primary: 35B25, 35J30, 35J35, 35J91

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 7/8 • July/August 2015
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