On poisson operators and dirichlet-neumann maps in H^s for divergence form elliptic operators with lipschitz coefficients

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∈[0,1]. Moreover, we also show a factorizationformula for the elliptic operator in terms of the Poisson operator.