On Poisson operators and Dirichlet-Neumann maps in H^s for divergence form elliptic operators with Lipschitz coefficients

Abstract

We consider second order uniformly elliptic operators of divergence form in ${\mathbb{R}}^{d+1}$ 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 $H^s({\mathbb{R}}^d)$ for each $s\in [0,1]$. Moreover, we also show a factorization formula for the elliptic operator in terms of the Poisson operator.

References in corpus (2)

• Analyticity of layer potentials and $L^2$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty }$ coefficients
• On domain of Poisson operators and factorization for divergence form elliptic operators