Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball

DOI10.1007/s10958-010-0045-4zbMath1222.31003OpenAlexW2083112632MaRDI QIDQ548731

Gershon I. Kresin, Vladimir Gilelevich Maz'ya

Publication date: 30 June 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0045-4

zbMATH Keywords

harmonic function

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05)

Related Items (15)

A Khavinson type conjecture for hyperbolic harmonic functions on the unit ball ⋮ Sharp estimates for the gradient of the generalized Poisson integral for a half-space ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Optimal estimates for the gradient of harmonic functions in the unit disk ⋮ Optimal estimates for harmonic functions in the unit ball ⋮ Khavinson problem for hyperbolic harmonic mappings in Hardy space ⋮ PMA celebrates the 85th birthday of V. G. Maz'ya ⋮ Generalized Poisson integral and sharp estimates for harmonic and biharmonic functions in the half-space ⋮ Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions ⋮ Schwarz lemma for harmonic mappings in the unit ball ⋮ Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions ⋮ Solution to the Khavinson problem near the boundary of the unit ball ⋮ Heinz-Schwarz inequalities for harmonic mappings in the unit ball ⋮ A proof of the Khavinson conjecture ⋮ A proof of the Khavinson conjecture in \(\mathbb{R}^3\)

Cites Work

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• Optimal estimates for the gradient of harmonic functions in the multidimensional half-space
• A Schwarz lemma for harmonic and hyperbolic-harmonic functions in higher dimensions
• An Extremal Problem for Harmonic Functions in the Ball
• Gradient bounds for harmonic functions lipschitz on the boundary

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