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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 |
URI: | http://www.sciencedirect.com/science/article/pii/S0022247X1200858X http://bura.brunel.ac.uk/handle/2438/7239 |
DOI: | http://dx.doi.org/10.1016/j.jmaa.2012.10.045 |
ISSN: | 0022-247X |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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