Intrinsic geometries and boundary values of differentiable functions. I
Let G be an arbitrary domain in \(R^ n\). The author introduces an (anisotropic) intrinsic distance in G. With the help of this distance he characterizes in {\S} 1 some function spaces of Lipschitz-Nikolskij- Sobolev type in G. In {\S} 2 he studies boundary values of functions belonging to these function spaces (when \(\partial G\) is smooth then these boundary values coincide with the usual boundary values). Of special interest is {\S} 3 in which the author studies the extension problem: How to construct a linear extension operator for the function spaces on G into the corresponding function spaces on \(R^ n\) (sufficient and necessary conditions generalizing known results).
function spaces of Lipschitz-Nikolskij-Sobolev type
scientific article; zbMATH DE number 4132885
scientific article