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...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
|
| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/124447 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-124447 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1244472017-09-27T03:03:11Z On the Shapiro-Lopatinkii condition for elliptic problem Dyachenko, E. 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. 2014 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/124447 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Dyachenko, E. |
| spellingShingle |
Dyachenko, E. On the Shapiro-Lopatinkii condition for elliptic problem Український математичний вісник |
| author_facet |
Dyachenko, E. |
| author_sort |
Dyachenko, E. |
| title |
On the Shapiro-Lopatinkii condition for elliptic problem |
| title_short |
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_sort |
on the shapiro-lopatinkii condition for elliptic problem |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/124447 |
| 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. |
| series |
Український математичний вісник |
| work_keys_str_mv |
AT dyachenkoe ontheshapirolopatinkiiconditionforellipticproblem |
| first_indexed |
2023-10-18T20:46:25Z |
| last_indexed |
2023-10-18T20:46:25Z |
| _version_ |
1796151072416333824 |