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arXiv · 1805.08528

Sobolev-like Hilbert spaces induced by elliptic operators

Tetiana Kasirenko·Vladimir Mikhailets·Aleksandr Murach
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Abstract

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 $\overline{\Omega}$. The domain and the coefficients of $A$ are of the class $C^{\infty}$. These spaces consist of all distributions $u\in H^{s}(\Omega)$ such that $Au\in H^{\lambda}(\Omega)$ and are endowed with the corresponding graph norm, with $s,\lambda\in\mathbb{R}$. We prove an interpolation formula for these spaces and discuss their application to elliptic boundary-value problems.

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Tetiana Kasirenko, Vladimir Mikhailets, Aleksandr Murach. 2018-05-22. Sobolev-like Hilbert spaces induced by elliptic operators. https://doi.org/10.1007/s11785-018-00886-8

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