  We consider second order uniformly elliptic operators of divergence form in
$\R^{d+1}$ whose coefficients are independent of one variable. For such a class
of operators we establish a factorization into a product of first order
operators related with Poisson operators and Dirichlet-Neumann maps.
Consequently, we obtain a solution formula for the inhomogeneous elliptic
boundary value problem in the half space, which is useful to show the existence
of solutions in a wider class of inhomogeneous data. We also establish $L^2$
solvability of boundary value problems for a new class of the elliptic
operators.
