Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity
For divergent elliptic equations with the natural energetic spaceW p m (Ω),m≥1,p>2, we prove that the Dirichlet problem is solvable in a broad class of domains with noncompact boundaries if the growth of the right-hand side of the equation is determined by the corresponding theorem of Phragm...
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| Datum: | 1995 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5413 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511646292639744 |
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| author | Shishkov, A. E. Шишков, А. Е. Шишков, А. Е. |
| author_facet | Shishkov, A. E. Шишков, А. Е. Шишков, А. Е. |
| author_sort | Shishkov, A. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:58:41Z |
| description | For divergent elliptic equations with the natural energetic spaceW p m (Ω),m≥1,p>2, we prove that the Dirichlet problem is solvable in a broad class of domains with noncompact boundaries if the growth of the right-hand side of the equation is determined by the corresponding theorem of Phragmén-Lindelöf type. For the corresponding parabolic equation, we prove that the Cauchy problem is solvable for the limiting growth of the initial function % MathType!MTEF!2!1!+- $$u_0 (x) \in L_{2.loc} (R^n ): \int\limits_{|x|< \tau } {u_0^2 dx \leqslant c\tau ^{n + 2mp/(p - 2)} \forall \tau< \infty } $$ |
| first_indexed | 2026-03-24T03:16:12Z |
| format | Article |
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| id | umjimathkievua-article-5413 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:16:12Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3c/a992229b51d05938a89c53bc83fb7f3c.pdf |
| spelling | umjimathkievua-article-54132020-03-19T08:58:41Z Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity Разрешимость граничных задач для квазилинейных эллиптических и параболических уравнений в неограниченных областях в классах функций, растущих на бесконечности Shishkov, A. E. Шишков, А. Е. Шишков, А. Е. For divergent elliptic equations with the natural energetic spaceW p m (Ω),m≥1,p>2, we prove that the Dirichlet problem is solvable in a broad class of domains with noncompact boundaries if the growth of the right-hand side of the equation is determined by the corresponding theorem of Phragmén-Lindelöf type. For the corresponding parabolic equation, we prove that the Cauchy problem is solvable for the limiting growth of the initial function % MathType!MTEF!2!1!+- $$u_0 (x) \in L_{2.loc} (R^n ): \int\limits_{|x|< \tau } {u_0^2 dx \leqslant c\tau ^{n + 2mp/(p - 2)} \forall \tau< \infty } $$ Для дивергентних еліптичних рівнянь з природним енергетичним простором $W_p^m (Ω), m ≥ 1, p > 2$, встановлено існування розв'язку задачі Діріхле в широкому класі областей з некомпактними границями при зростанні правої частини рівняння, що визначається відповідною теоремою типу теореми Фрагмена-Ліндельофа. Для відповідного параболічного рівняння доведена розв'язуваність задачі Коші при граничному зростанні початкової функції $$u_0 (x) \in L_{2.loc} (R^n ): \int\limits_{|x|< \tau } {u_0^2 dx \leqslant c\tau ^{n + 2mp/(p - 2)} \forall \tau< \infty }$$ Institute of Mathematics, NAS of Ukraine 1995-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5413 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 2 (1995); 277–289 Український математичний журнал; Том 47 № 2 (1995); 277–289 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5413/7515 https://umj.imath.kiev.ua/index.php/umj/article/view/5413/7516 Copyright (c) 1995 Shishkov A. E. |
| spellingShingle | Shishkov, A. E. Шишков, А. Е. Шишков, А. Е. Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title | Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title_alt | Разрешимость граничных задач для квазилинейных эллиптических и параболических уравнений в неограниченных областях в классах функций, растущих на бесконечности |
| title_full | Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title_fullStr | Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title_full_unstemmed | Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title_short | Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| title_sort | solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5413 |
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