Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

Details Sharp Growth Estimates for Modified Poisson Integrals in a Half Space Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

2001-01-02

arxiv.org/abs/math/0101016v1

Mathematics

Classical Analysis and ODEs

To appear in Potential Analysis, 28 pages

Scientific paper

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.

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