On domain of Poisson operators and factorization for divergence form elliptic operators

Abstract

We consider second order uniformly elliptic operators of divergence form in ${\mathbb{R}}^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators related with Poisson operators and Dirichlet-Neumann maps. Consequently, we obtain a solution formula for the inhomogeneous elliptic boundary value problem in the half space, which is useful to show the existence of solutions in a wider class of inhomogeneous data. We also establish $L^2$ solvability of boundary value problems for a new class of the elliptic operators.

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
• Remark on the Helmholtz decomposition in domains with noncompact boundary

Cited by in corpus (1)

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