Necessary and sufficient conditions for the solvability of the Gauss variational problem

被引：0

作者：

Zorii N.V. ^{[1
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2005年 / 57卷 / 1期

关键词：

Variational Problem; Limit Point; Compact Space; General Assumption; Radon Measure;

D O I：

10.1007/s11253-005-0172-0

中图分类号：

学科分类号：

摘要：

We investigate the well-known Gauss variational problem over classes of Radon measures associated with a system of sets in a locally compact space. Under fairly general assumptions, we obtain necessary and sufficient conditions for its solvability. As an auxiliary result, we describe the potentials of vague and (or) strong limit points of minimizing sequences of measures. The results obtained are also specified for the Newton kernel in ℝ n. © 2005 Springer Science+Business Media, Inc.

引用

页码：70 / 99

页数：29

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