Elliptic B. Lawruk boundary value problems in the extended Sobolev scale
In the extended Sobolev scale, we investigate a class of elliptic problems with additional unknown functions in boundary conditions, which is introduced by B.~Lawruk. This scale consists of all Hilbert spaces that are interpolation spaces for pairs of Sobolev inner-product spaces and, moreover, admi...
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| Date: | 2015 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
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Інститут математики НАН України
2015
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/204 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | In the extended Sobolev scale, we investigate a class of elliptic problems with additional unknown functions in boundary conditions, which is introduced by B.~Lawruk. This scale consists of all Hilbert spaces that are interpolation spaces for pairs of Sobolev inner-product spaces and, moreover, admits a constructive description in terms of H\"ormander spaces. We prove a theorem on the Fredholm property of the bounded operators corresponding to these problems on the extended Sobolev scale and a theorem on local regularity of their solutions in H\"ormander spaces. We find sufficient conditions under which the generalized derivatives (of a given order) of the solutions are continuous. |
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