  We consider second order uniformly elliptic operators of divergence form in
$\R^{d+1}$ whose coefficients are independent of one variable. Under the
Lipschitz condition on the coefficients we characterize the domain of the
Poisson operators and the Dirichlet-Neumann maps in the Sobolev space
$H^s(\R^d)$ for each $s\in [0,1]$. Moreover, we also show a factorization
formula for the elliptic operator in terms of the Poisson operator.

Analysis of PDEs