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
Datum:2014
1. Verfasser: Dyachenko, E.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/124447
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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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-124447
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
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
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