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For functions from the Sobolev space $H^s(\Omega)$, 1/2<s<3/2, definitions ofnon-unique generalised and unique canonical co-normal derivative areconsidered, which are related to possible extensions of a partial differentialoperator and its right hand side from the domain $\Omega$, where they areprescribed, to the domain boundary, where they are not. Revision of theboundary value problem settings, which makes them insensitive to the co-normalderivative inherent non-uniqueness are given. Some new facts about traceoperator estimates, Sobolev spaces characterisations, and solution regularityof PDEs with non-smooth coefficients are also presented.

Traces, extensions, co-normal derivatives and solution regularity of elliptic systems with smooth and non-smooth coefficients