On Poisson operators and Dirichlet-Neumann maps in Hs 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 Hs (ℝ d ) for each s ∈ [0, 1]. Moreover, we also show a factorization formula for the elliptic operator in terms of the Poisson operator. 2010 Mathematics Subject Classification. Primary 35J15, 35J25, 35S05. Key words and phrases. Divergence form elliptic operators, Poisson operators, Dirichlet-Neumann maps.