Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

Abstract

For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in ${\mathbb{R}}^n$. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems.

To appear in Potential Analysis, 28 pages