ON POISSON OPERATORS AND DIRICHLET-NEUMANN MAPS IN H-s FOR DIVERGENCE FORM ELLIPTIC OPERATORS WITH LIPSCHITZ COEFFICIENTS

摘要

We consider second order uniformly elliptic operators of divergence form in Rd+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 is an element of [0, 1]. Moreover, we also show a factorization formula for the elliptic operator in terms of the Poisson operator.