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.

引用

页码：177 / 203

页数：27

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