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.
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