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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
ISSN: 0022-247X
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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