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
收藏
页码：425 / 440
页数：16
相关论文
共 50 条
12345