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Zbl 0987.31003
Siegel, David; Talvila, Erik
Sharp growth estimates for modified Poisson integrals in a half space. (English)
[J] Potential Anal. 15, No.4, 333-360 (2001). ISSN 0926-2601; ISSN 1572-929X/e

The authors use modified Poisson integrals in order to write solutions to the half space Dirichlet and Neumann problems in ${\Bbb R}^n$ with continuous boundary data, including data of polynomial growth. Pointwise growth estimates are given for these integrals which are 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.
[Dian K.Palagachev (Bari)]

MSC 2000:: *31B10 Integral representations of harmonic functions (higher-dimensional)
35J05 Laplace equation, etc.
31B20 Boundary value and inverse problems (higher-dim. potential theory)

Keywords: Poisson integral; half space Dirichlet and Neumann problems

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