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Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

David Siegel·Erik Talvila
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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.

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David Siegel, Erik Talvila. 2001-01-02. Sharp Growth Estimates for Modified Poisson Integrals in a Half Space. https://arxiv.org/abs/math/0101016

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