Calculus of Variations and Geometric Measure Theory

E. Berchio - F. Gazzola - T. Weth

Critical growth biharmonic elliptic problems under Steklov-type boundary conditions

created by gazzola on 16 Feb 2006
modified on 18 Jan 2007

[BibTeX]

Accepted Paper

Inserted: 16 feb 2006
Last Updated: 18 jan 2007

Year: 2006

Abstract:

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


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