Regularity of the extremal solution for a fourthorder elliptic problem with singular nonlinearity
Baishun Lai  Institute of Contemporary Mathematics, Henan University, School of Mathematics and Information Science, Henan University, Kaifeng 475004, China (email) Abstract: In this paper, we consider the relation between $p > 1$ and critical dimension of the extremal solution of the semilinear equation
$\beta \Delta^{2}u\tau \Delta u=\frac{\lambda}{(1u)^{p}} \mbox{in} B$, where $B$ is the unit ball in $R^{n}$, $\lambda>0$ is a parameter, $\tau>0, \beta>0,p>1$ are fixed constants. By HardyRellich inequality, we find that when $p$ is large enough, the critical dimension is 13.
Keywords: Minimal solutions, regularity, critical dimension, stability, fourth order.
Received: January 2010; Revised: May 2010; Available Online: February 2011. 
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