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Title: | Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains |
Authors: | Mikhailov, SE |
Keywords: | Partial differential equation systems;Sobolev spaces;Classical, generalized and canonical co-normal derivatives;Weak BVP settings |
Issue Date: | 2011 |
Publisher: | Elsevier |
Citation: | Journal of Mathematical Analysis and Applications 378(1): 324 - 342, Jun 2011 |
Abstract: | For functions from the Sobolev space H^s(\Omega), 1/2 < s < 3/2 , definitions of non-unique generalized and unique canonical co-normal derivative are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domain, where they are prescribed, to the domain boundary, where they are not. Revision of the boundary value problem settings, which makes them insensitive to the generalized co-normal derivative inherent non-uniqueness are given. It is shown, that the canonical co-normal derivatives, although de¯ned on a more narrow function class than the generalized ones, are continuous extensions of the classical co-norma derivatives. Some new results about trace operator estimates and Sobolev spaces haracterizations, are also presented. |
Description: | This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2011 Elsevier |
URI: | http://bura.brunel.ac.uk/handle/2438/5913 |
DOI: | http://dx.doi.org/10.1016/j.jmaa.2010.12.027 |
ISSN: | 0022-247X |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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Mikhailov-JMAA2011-6.pdf | 206.72 kB | Adobe PDF | View/Open |
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