On the Shapiro-Lopatinkii condition for elliptic problem
This paper is concerned with elliptic problems including a small parameter multiplying higher order derivatives. We found algebraic conditions on the operator and boundary conditions which guarantee the Fredholm property, and prove an a priori estimate for the solution with a constant independent of...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124447 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Shapiro-Lopatinkii condition for elliptic problem / E. Dyachenko // Український математичний вісник. — 2014. — Т. 11, № 1. — С. 49-68. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862740234977935360 |
|---|---|
| author | Dyachenko, E. |
| author_facet | Dyachenko, E. |
| citation_txt | On the Shapiro-Lopatinkii condition for elliptic problem / E. Dyachenko // Український математичний вісник. — 2014. — Т. 11, № 1. — С. 49-68. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | This paper is concerned with elliptic problems including a small parameter multiplying higher order derivatives. We found algebraic conditions on the operator and boundary conditions which guarantee the Fredholm property, and prove an a priori estimate for the solution with a constant independent of the small parameter. These results are known for elliptic boundary value problems with small parameter in the half space Rⁿ+. We extend them to the case of bounded domains with smooth boundary. The small parameter coercive conditions are formulated and two-sided estimate is proved.
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| first_indexed | 2025-12-07T20:13:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124447 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T20:13:56Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dyachenko, E. 2017-09-26T14:06:43Z 2017-09-26T14:06:43Z 2014 On the Shapiro-Lopatinkii condition for elliptic problem / E. Dyachenko // Український математичний вісник. — 2014. — Т. 11, № 1. — С. 49-68. — Бібліогр.: 12 назв. — англ. 1810-3200 2010 MSC. 58J37. https://nasplib.isofts.kiev.ua/handle/123456789/124447 This paper is concerned with elliptic problems including a small parameter multiplying higher order derivatives. We found algebraic conditions on the operator and boundary conditions which guarantee the Fredholm property, and prove an a priori estimate for the solution with a constant independent of the small parameter. These results are known for elliptic boundary value problems with small parameter in the half space Rⁿ+. We extend them to the case of bounded domains with smooth boundary. The small parameter coercive conditions are formulated and two-sided estimate is proved. I thank Professor Nikolai Tarkhanov for the proposed problem, his useful remarks and suggestions. en Інститут прикладної математики і механіки НАН України Український математичний вісник On the Shapiro-Lopatinkii condition for elliptic problem Article published earlier |
| spellingShingle | On the Shapiro-Lopatinkii condition for elliptic problem Dyachenko, E. |
| title | On the Shapiro-Lopatinkii condition for elliptic problem |
| title_full | On the Shapiro-Lopatinkii condition for elliptic problem |
| title_fullStr | On the Shapiro-Lopatinkii condition for elliptic problem |
| title_full_unstemmed | On the Shapiro-Lopatinkii condition for elliptic problem |
| title_short | On the Shapiro-Lopatinkii condition for elliptic problem |
| title_sort | on the shapiro-lopatinkii condition for elliptic problem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124447 |
| work_keys_str_mv | AT dyachenkoe ontheshapirolopatinkiiconditionforellipticproblem |