Homogeneous elliptic equations in an extended Sobolev scale
DOI:
https://doi.org/10.15407/dopovidi2018.03.003Keywords:
elliptic equation, Fredholm operator, Hörmander space, interpolation space, regularity of a solution, Sobolev spaceAbstract
In an extended Sobolev scale, we investigate homogeneous elliptic differential equations, whose solutions satisfy general enough boundary conditions. This scale consists of isotropic Hilbertian Hörmander spaces for which the regularity index is an arbitrary function RO-varying at infinity in the sense of Avakumović. We establish theorems on the character of solvability of these equations and the local regularity (up to the boundary of the domain) of their solutions in the scale indicated. We give an explicit description of all Hilbert spaces that are interpolation ones for pairs of subspaces of Hilbert Sobolev spaces formed by solutions of a homogeneous elliptic equation.
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