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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| Veröffentlicht in: | Український математичний вісник |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Zugang: | 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 |
| Zitieren: | On the Shapiro-Lopatinkii condition for elliptic problem / E. Dyachenko // Український математичний вісник. — 2014. — Т. 11, № 1. — С. 49-68. — Бібліогр.: 12 назв. — англ. |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the Shapiro-Lopatinkii condition for elliptic problem |
| spellingShingle |
On the Shapiro-Lopatinkii condition for elliptic problem Dyachenko, E. |
| 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 |
| author |
Dyachenko, E. |
| author_facet |
Dyachenko, E. |
| publishDate |
2014 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT dyachenkoe ontheshapirolopatinkiiconditionforellipticproblem |
| first_indexed |
2025-12-07T20:13:56Z |
| last_indexed |
2025-12-07T20:13:56Z |
| _version_ |
1850881800953397248 |