Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

Gershon Kresin; Vladimir Maz'ya

doi:10.3934/dcds.2010.28.425

Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

Gershon Kresin, Vladimir Maz'ya

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to L^p. This representation is concretized for the cases p = 1, 2, and ∞.

Original language	English
Pages (from-to)	425-440
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	28
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2010.28.425
State	Published - Oct 2010

Keywords

Estimates of the gradient
Khavinson's problem
Multidimensional harmonic functions
Real-part theorems

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10.3934/dcds.2010.28.425

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title = "Optimal estimates for the gradient of harmonic functions in the multidimensional half-space",

abstract = "A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to Lp. This representation is concretized for the cases p = 1, 2, and ∞.",

keywords = "Estimates of the gradient, Khavinson's problem, Multidimensional harmonic functions, Real-part theorems",

author = "Gershon Kresin and Vladimir Maz'ya",

year = "2010",

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AB - A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to Lp. This representation is concretized for the cases p = 1, 2, and ∞.

KW - Estimates of the gradient

KW - Khavinson's problem

KW - Multidimensional harmonic functions

KW - Real-part theorems

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JO - Discrete and Continuous Dynamical Systems

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Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

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