Bounded Extremal and Cauchy-Laplace Problems on the Sphere and Shell

被引：14
|
作者：
Atfeh, Bilal [2 ]
Baratchart, Laurent [2 ]
Leblond, Juliette [2 ]
Partington, Jonathan R. [1 ]
机构：
[1] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England
[2] INRIA, F-06902 Sophia Antipolis, France
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2010年 / 16卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Harmonic functions; Hardy classes; Extremal problems; Inverse Dirichlet-Neumann problems; CONSTRAINED APPROXIMATION; HARDY-APPROXIMATION; RIESZ TRANSFORMS; SUBSETS;
D O I：
10.1007/s00041-009-9110-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we develop a theory of approximating general vector fields on subsets of the sphere in a"e (n) by harmonic gradients from the Hardy space H (p) of the ball, 1 < p < a. This theory is constructive for p=2, enabling us to solve approximate recovery problems for harmonic functions from incomplete boundary values. An application is given to Dirichlet-Neumann inverse problems for n=3, which are of practical importance in medical engineering. The method is illustrated by two numerical examples.
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页码：177 / 203
页数：27
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