Generalized Poisson integral and sharp estimates for harmonic and biharmonic functions in the half-space

DOI10.1051/MMNP/2018032zbMath1411.31004arXiv1709.03412OpenAlexW2963534238MaRDI QIDQ4615696

Gershon I. Kresin, Vladimir Gilelevich Maz'ya

Publication date: 29 January 2019

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03412

zbMATH Keywords

harmonic functionssharp estimatesgeneralized Poisson integralbiharmonic functions.two-parametric kernel

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (3)

Unnamed Item ⋮ Sharp estimates for the gradient of solutions to the heat equation ⋮ Some extremal problems for solutions of the modified Helmholtz equation in the half-space

Cites Work

• Unnamed Item
• Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball
• Optimal estimates for the gradient of harmonic functions in the multidimensional half-space
• Invariant convex bodies for strongly elliptic systems
• Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions
• An Extremal Problem for Harmonic Functions in the Ball
• A simple solution method for the first boundary value problem of the polyharmonic equation

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