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arXiv · 1812.02700

H\"ormander spaces on manifolds, and their application to elliptic boundary-value problems

T. M. Kasirenko·A. A. Murach·I. S. Chepurukhina
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Abstract

We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product H\"ormander spaces for which an RO-varying radial function serves as a regularity index. These spaces do not depend on a choice of local charts on the manifold. The scale consists of all Hilbert spaces that are interpolation ones for pairs of inner-product Sobolev spaces, is obtained by the interpolation with a function parameter of these pairs, and is closed with respect to this interpolation. As an application of the scale introduced, we give a theorem on the Fredholm property of a general elliptic boundary-value problem on appropriate H\"ormander spaces and find sufficient conditions under which its generalized solutions belong to the space of $p\geq0$ times continuously differential functions.

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T. M. Kasirenko, A. A. Murach, I. S. Chepurukhina. 2018-12-06. H\"ormander spaces on manifolds, and their application to elliptic boundary-value problems. https://doi.org/10.15407/dopovidi2019.03.009

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