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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| Published in: | Український математичний вісник |
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| Date: | 2014 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124447 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1810-3200 |