Title | Hörmander spaces on manifolds, and their application to elliptic boundaryvalue problems |
Publication Type | Journal Article |
Year of Publication | 2019 |
Authors | Kasirenko, TM, Murach, AA, Chepurukhina, IS |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2019.03.009 |
Issue | 3 |
Section | Mathematics |
Pagination | 9-16 |
Date Published | 03/2019 |
Language | Ukrainian |
Abstract | We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by innerproduct Hörmander spaces, for which a radial function ROvarying in the sense of Avakumovic 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 innerproduct 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 bounda ryvalue problem on appropriate Hörmander spaces and find sufficient conditions, under which its generalized solutions belong to the space of p 0 times continuously differentiable functions. |
Keywords | elliptic boundaryvalue problem., extended Sobolev scale, Hörmander space, interpolation between spaces, interpolation space |
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