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Title: Solution regularity and co-normal derivatives for elliptic systems with non-smooth coefficients on Lipschitz domains
Authors: Mikhailov, SE
Keywords: Partial differential equation systems;Non-smooth coefficients;Sobolev spaces;Solution regularity;Classical, generalized and canonical co-normal derivatives;Weak BVP settings
Issue Date: 2013
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications, 400(1): 48 - 67, Apr 2013
Abstract: Elliptic PDE systems of the second order with coefficients from L∞ or Holder-Lipschitz spaces are considered in the paper. Continuity of the operators in corresponding Sobolev spaces is stated and the internal (local) solution regularity theorems are generalized to the non-smooth coefficient case. For functions from the Sobolev space H^s(Omega), 0.5<s<1.5, 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 the PDE right hand side from the domain $\Omega$ to its boundary. It is proved that the canonical co-normal derivatives coincide with the classical ones when both exist. A generalization of the boundary value problem settings, which makes them insensitive to the co-normal derivative inherent non-uniqueness is given.
Description: This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 Elsevier
ISSN: 0022-247X
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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