Sobolev-Like Hilbert Spaces Induced by Elliptic Operators

摘要

We investigate properties of function spaces induced by the inner product Sobolev spaces H-s(Omega) over a bounded Euclidean domain Omega and by an elliptic differential operator A on (Omega) over bar. The domain and the coefficients of A are of the class C-infinity. These spaces consist of all distributions u is an element of H-s(Omega) such that Au is an element of H-lambda(Omega) and are endowed with the corresponding graph norm, with s, lambda is an element of R. We prove an interpolation formula for these spaces and discuss their application to elliptic boundary-value problems.