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 Hs(Rd) for each s∈[0,1]. Moreover, we also show a factorizationformula for the elliptic operator in terms of the Poisson operator.
- DirichletNeumann maps
- Divergence form elliptic operators
- Poisson operators
ASJC Scopus subject areas
- Applied Mathematics