Hörmander spaces on manifolds, and their application to elliptic boundaryvalue problems
DOI:
https://doi.org/10.15407/dopovidi2019.03.009Keywords:
elliptic boundaryvalue problem., extended Sobolev scale, Hörmander space, interpolation between spaces, interpolation spaceAbstract
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 p0 times continuously differentiable functions.
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