Article Contents
Article Contents

# Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity

• In this paper, we consider the relation between $p > 1$ and critical dimension of the extremal solution of the semilinear equation

$\beta \Delta^{2}u-\tau \Delta u=\frac{\lambda}{(1-u)^{p}} \mbox{in} B$,
$0 < u \leq 1 \mbox{in} B$,
$u=\Delta u=0 \mbox{on} \partial B$,

where $B$ is the unit ball in $R^{n}$, $\lambda>0$ is a parameter, $\tau>0, \beta>0,p>1$ are fixed constants. By Hardy-Rellich inequality, we find that when $p$ is large enough, the critical dimension is 13.

Mathematics Subject Classification: Primary 35B45; Secondary 35J40.

 Citation:

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