Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains

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Abstract

For functions from the Sobolev space Hs(ω), 12<s<32, 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 ω, 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 defined on a more narrow function class than the generalized ones, are continuous extensions of the classical co-normal derivatives. Some new results about trace operator estimates and Sobolev spaces characterizations, are also presented. © 2010 Elsevier Inc.

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Mikhailov, S. E. (2011). Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains. Journal of Mathematical Analysis and Applications, 378(1), 324–342. https://doi.org/10.1016/j.jmaa.2010.12.027

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