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

共 50 条

[1] Bounded Extremal and Cauchy–Laplace Problems on the Sphere and Shell
Bilal Atfeh
Laurent Baratchart
Juliette Leblond
Jonathan R. Partington
Journal of Fourier Analysis and Applications, 2010, 16 : 177 - 203
[2] A cauchy-laplace multifractal wavelet model for network redundant traffic
Xing, Ling
Ma, Qiang
Xu, Lei
Jiang, Chun-Xiao
Beijing Youdian Daxue Xuebao/Journal of Beijing University of Posts and Telecommunications, 2015, 38 (05): : 54 - 57
[3] Problems on Extremal Decomposition of the Riemann Sphere
G. V. Kuz'mina
Journal of Mathematical Sciences, 2003, 118 (1) : 4880 - 4894
[4] A CONVERSE OF CAUCHY THEOREM AND APPLICATIONS TO EXTREMAL PROBLEMS
READ, AH
ACTA MATHEMATICA, 1958, 100 (1-2) : 1 - 22
[5] FRACTIONAL CAUCHY PROBLEMS ON BOUNDED DOMAINS
Meerschaert, Mark M.
Nane, Erkan
Vellaisamy, P.
ANNALS OF PROBABILITY, 2009, 37 (03): : 979 - 1007
[6] Cauchy problems for Laplace equation on compact sets
Titarenko, VN
Yagola, AG
INVERSE PROBLEMS IN ENGINEERING, 2002, 10 (03): : 235 - 254
[7] BOUNDED MODULES, EXTREMAL PROBLEMS, AND A CURVATURE INEQUALITY
MISRA, G
SASTRY, NSN
JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) : 118 - 134
[8] Extremal problems for transversals in graphs with bounded degree
Szabo, Tibor
Tardos, Gabor
COMBINATORICA, 2006, 26 (03) : 333 - 351
[9] MAGNETIC MOMENT ESTIMATION AND BOUNDED EXTREMAL PROBLEMS
Baratghart, Laurent
Chevillard, Sylvain
Hardin, Douglas
Leblond, Juliette
Lima, Eduardo Andrade
Marmorat, Jean-Paul
INVERSE PROBLEMS AND IMAGING, 2019, 13 (01) : 39 - 67
[10] EXTREMAL PROBLEMS FOR FUNCTIONS OF BOUNDED BOUNDARY ROTATION
PINCHUK, B
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (05) : 708 - &

← 1 2 3 4 5 →