Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

2001/01/02 by David Siegel, Siegel, David, Erik Talvila +1
Computer Science · Mathematics · #31B10 #35J05 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Meromorphic and Entire Functions #advanced mathematical theories #math.CA #msc:31B10 #msc:35J05

paper · pdf · doi:10.48550/arxiv.math/0101016

To appear in Potential Analysis, 28 pages

arxiv created 2001/01/02 · openalex publication_date 2001/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℝⁿ. 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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