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2007 Critical growth biharmonic elliptic problems under Steklov-type boundary conditions
Elvise Berchio, Filippo Gazzola, Tobias Weth
Adv. Differential Equations 12(4): 381-406 (2007).

Abstract

We study the fourth-order nonlinear critical problem $\Delta^2 u= u^{2^*-1}$ in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$, $n \ge 5$, subject to the boundary conditions $u=\Delta u-d u_\nu=0$ on $\partial \Omega$. We provide estimates for the range of parameters $d \in \mathbb{R}$ for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description.

Citation

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Elvise Berchio. Filippo Gazzola. Tobias Weth. "Critical growth biharmonic elliptic problems under Steklov-type boundary conditions." Adv. Differential Equations 12 (4) 381 - 406, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1155.35018
MathSciNet: MR2305873

Subjects:
Primary: 35J40
Secondary: 35B33, 47J30

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 4 • 2007
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