Elliptic problems and Hörmander spaces

Vladimir A. Mikhailets; Aleksandr A. Murach

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arXiv · 0904.0372

Elliptic problems and Hörmander spaces

Vladimir A. Mikhailets·Aleksandr A. Murach

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Abstract

The paper gives a survey of the modern results on elliptic problems on the Hörmander function spaces. More precisely, elliptic problems are studied on a Hilbert scale of the isotropic Hörmander spaces parametrized by a real number and a function slowly varying at $+\infty$ in the Karamata sense. This refined scale is finer than the Sobolev scale and is closed with respect to the interpolation with a function parameter. The Fredholm property of elliptic operators and elliptic boundary-value problems is preserved for this scale. A local refined smoothness of the elliptic problem solution is studied. An abstract construction of classes of function spaces in which the elliptic problem is a Fredholm one is found. In particular, some generalizations of the Lions-Magenes theorems are given.

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BibTeX RIS

Vladimir A. Mikhailets, Aleksandr A. Murach. 2009-04-02. Elliptic problems and Hörmander spaces. https://arxiv.org/abs/0904.0372

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