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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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.

Article information

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867456

Mathematical Reviews number (MathSciNet)
MR2305873

Zentralblatt MATH identifier
1155.35018

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

Citation

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. https://projecteuclid.org/euclid.ade/1355867456


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