Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator
In a special class of domains in an infinite-dimensional Hilbert space, the solvability of the Dirichlet problem for the Poisson equation with an elliptic operator of the form $(Lu)(x)=j(x)(u''(x))$ vanishing on cylindrical functions is proved.
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| Datum: | 1994 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5670 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511897118310400 |
|---|---|
| author | Bogdanskii, Yu. V. Богданский, Ю. В. Богданский, Ю. В. |
| author_facet | Bogdanskii, Yu. V. Богданский, Ю. В. Богданский, Ю. В. |
| author_sort | Bogdanskii, Yu. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:15:43Z |
| description | In a special class of domains in an infinite-dimensional Hilbert space, the solvability of the Dirichlet
problem for the Poisson equation with an elliptic operator of the form $(Lu)(x)=j(x)(u''(x))$
vanishing on cylindrical functions is proved. |
| first_indexed | 2026-03-24T03:20:11Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5670 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:20:11Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c6/d8883c0b0e67f395bfe33e9b51a6abc6.pdf |
| spelling | umjimathkievua-article-56702020-03-19T09:15:43Z Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator Задача Дирихле для уравнения Пуассона с существенно бесконечномерным эллиптическим оператором Bogdanskii, Yu. V. Богданский, Ю. В. Богданский, Ю. В. In a special class of domains in an infinite-dimensional Hilbert space, the solvability of the Dirichlet problem for the Poisson equation with an elliptic operator of the form $(Lu)(x)=j(x)(u''(x))$ vanishing on cylindrical functions is proved. У спеціальному класі областей нескінченновимірного гільбертового простору доведена розв’язність задачі Діріхле для рівняння Пуассона з еліптичним оператором, що має вигляд $(Lu)(x)=j(x)(u''(x))$ та дорівнює нулю на циліндричних функціях. Institute of Mathematics, NAS of Ukraine 1994-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5670 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 7 (1994); 803–808 Український математичний журнал; Том 46 № 7 (1994); 803–808 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5670/8025 https://umj.imath.kiev.ua/index.php/umj/article/view/5670/8026 Copyright (c) 1994 Bogdanskii Yu. V. |
| spellingShingle | Bogdanskii, Yu. V. Богданский, Ю. В. Богданский, Ю. В. Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title | Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title_alt | Задача Дирихле для уравнения Пуассона с существенно бесконечномерным эллиптическим оператором |
| title_full | Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title_fullStr | Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title_full_unstemmed | Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title_short | Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator |
| title_sort | dirichlet problem for the poisson equation with an essentially infinite-dimensional elliptic operator |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5670 |
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