  The aim of this paper is to establish some properties of solutions to the
Dirichlet-Neumann problem: $(\partial_z\partial_{\overline{z}})^2 w=g$ in the
unit disc $\ID$, $w=\gamma_0$ and
$\partial_{\nu}\partial_z\partial_{\overline{z}}w=\gamma$ on $\mathbb{T}$ (the
unit circle), $\frac{1}{2\pi
i}\int_{\mathbb{T}}w_{\zeta\overline{\zeta}}(\zeta)\frac{d\zeta}{\zeta}=c$,
where $\partial_\nu$ denotes differentiation in the outward normal direction.
More precisely, we obtain Schwarz-Pick type inequalities and Landau type
theorem for solutions to the Dirichlet-Neumann problem.
