Advances in Differential Equations

Critical growth biharmonic elliptic problems under Steklov-type boundary conditions

Elvise Berchio, Filippo Gazzola, and Tobias Weth

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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.

Article information

Adv. Differential Equations, Volume 12, Number 4 (2007), 381-406.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 35B33: Critical exponents 47J30: Variational methods [See also 58Exx]


Berchio, Elvise; Gazzola, Filippo; Weth, Tobias. Critical growth biharmonic elliptic problems under Steklov-type boundary conditions. Adv. Differential Equations 12 (2007), no. 4, 381--406.

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