Sobolev-like Hilbert spaces induced by elliptic operators

We investigate properties of function spaces induced by the inner product Sobolev spaces $H^{s}(Ω)$ over a bounded Euclidean domain $Ω$ and by an elliptic differential operator $A$ on $\overlineΩ$. The domain and the coefficients of $A$ are of the class $C^{\infty}$. These spaces consist of all distributions $u\in H^{s}(Ω)$ such that $Au\in H^λ(Ω)$ and are endowed with the corresponding graph norm, with $s,λ\in\mathbb{R}$. We prove an interpolation formula for these spaces and discuss their application to elliptic boundary-value problems.

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