Equilibrium Potentials with External Fields
We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals. Extremal problems dual to the original one are for...
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| Datum: | 2003 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3991 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510123458297856 |
|---|---|
| author | Zorii, N. V. Зорий, Н. В. Зорий, Н. В. |
| author_facet | Zorii, N. V. Зорий, Н. В. Зорий, Н. В. |
| author_sort | Zorii, N. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:03Z |
| description | We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals. Extremal problems dual to the original one are formulated and solved. The results obtained are new even in the case of classical kernels and the Euclidean space \(\mathbb{R}^n \) . |
| first_indexed | 2026-03-24T02:52:00Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3991 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:00Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5b/f69a79af5748ce16ff39e0497d43725b.pdf |
| spelling | umjimathkievua-article-39912020-03-18T20:18:03Z Equilibrium Potentials with External Fields Равновесные потенциалы с внешними полями Zorii, N. V. Зорий, Н. В. Зорий, Н. В. We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals. Extremal problems dual to the original one are formulated and solved. The results obtained are new even in the case of classical kernels and the Euclidean space \(\mathbb{R}^n \) . Досліджується варіаційна задача Гаусса над досить загальними класами мір Радона у локально компактному прос торі X. Отримано опис потенціалів мінімізуючих мір, виділено їх характеристичні властивості, доведено неперервність екстремалей. Знайдепо постановки екстремальних задач, дуальних до початкової. Отримані результат є новими навіть у випадку класичних ядер та евклідопого простору \(\mathbb{R}^n \) . Institute of Mathematics, NAS of Ukraine 2003-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3991 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 9 (2003); 1178-1195 Український математичний журнал; Том 55 № 9 (2003); 1178-1195 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3991/4694 https://umj.imath.kiev.ua/index.php/umj/article/view/3991/4695 Copyright (c) 2003 Zorii N. V. |
| spellingShingle | Zorii, N. V. Зорий, Н. В. Зорий, Н. В. Equilibrium Potentials with External Fields |
| title | Equilibrium Potentials with External Fields |
| title_alt | Равновесные потенциалы с внешними полями |
| title_full | Equilibrium Potentials with External Fields |
| title_fullStr | Equilibrium Potentials with External Fields |
| title_full_unstemmed | Equilibrium Potentials with External Fields |
| title_short | Equilibrium Potentials with External Fields |
| title_sort | equilibrium potentials with external fields |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3991 |
| work_keys_str_mv | AT zoriinv equilibriumpotentialswithexternalfields AT zorijnv equilibriumpotentialswithexternalfields AT zorijnv equilibriumpotentialswithexternalfields AT zoriinv ravnovesnyepotencialysvnešnimipolâmi AT zorijnv ravnovesnyepotencialysvnešnimipolâmi AT zorijnv ravnovesnyepotencialysvnešnimipolâmi |