OPTIMAL ESTIMATES FOR THE GRADIENT OF HARMONIC FUNCTIONS IN THE MULTIDIMENSIONAL HALF-SPACE

被引：12

作者：

Kresin, Gershon ^{[1
]}

Maz'ya, Vladimir ^{[2
,3
]}

机构：

[1] Ariel Univ Ctr Samaria, Dept Math & Comp Sci, IL-44837 Ariel, Israel

[2] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England

[3] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Real-part theorems; multidimensional harmonic functions; estimates of the gradient; Khavinson's problem;

D O I：

10.3934/dcds.2010.28.425

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 infinity.

引用

页码：425 / 440

页数：16

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