Bounded Extremal and Cauchy-Laplace Problems on the Sphere and Shell
Bounded Extremal and Cauchy-Laplace Problems on the Sphere and Shell
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球壳上的有界极值问题和柯西拉普拉斯问题
DOI：
10.1007/s00041-009-9110-0
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发表时间：
2009
影响因子：
1.2
通讯作者：
Atfeh B
中科院分区：
文献类型：
--
作者：
Atfeh B
本文从球的哈代空间H p（1<p<∞）出发，发展了一个用调和梯度逼近球面子集上一般向量场的理论.这个理论是建设性的forp=2，使我们能够解决近似恢复问题的调和函数从不完整的边界值。给出了在医学工程中具有实际意义的n =3的Dirichlet-Neumann反问题的一个应用.通过两个数值例子说明了该方法。
In this work, we develop a theory of approximating general vector fields on subsets of the sphere in ℝnby harmonic gradients from the Hardy spaceHpof the ball, 1<p<∞. This theory is constructive forp=2, enabling us to solve approximate recovery problems for harmonic functions from incomplete boundary values. An application is given to Dirichlet–Neumann inverse problems forn=3, which are of practical importance in medical engineering. The method is illustrated by two numerical examples.