Necessary and Sufficient Conditions for the Solvability of the Gauss Variational Problem
We investigate the well-known Gauss variational problem considered 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 po...
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| Datum: | 2005 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3574 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We investigate the well-known Gauss variational problem considered 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 potentials of vague and (or) strong limit points of minimizing sequences of measures.
The results obtained are also specified for the Newton kernel in $\mathbb{R}^n$. |
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