# H&ouml;rmander spaces on manifolds, and their application to elliptic boundaryvalue problems

 1Kasirenko, TM1Murach, AA1Chepurukhina, IS1Institute of Mathematics of the NAS of Ukraine, Kyiv Dopov. Nac. akad. nauk Ukr. 2019, 3:9-16 https://doi.org/10.15407/dopovidi2019.03.009 Section: Mathematics 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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