Hörmander spaces on manifolds, and their application to elliptic boundaryvalue problems

1Kasirenko, TM, 1Murach, AA, 1Chepurukhina, IS
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 3:9-16
Section: Mathematics
Language: Ukrainian

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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