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- Title
Petrovskii elliptic systems in the extended Sobolev scale.
- Authors
Zinchenko, Tetiana; Murach, Aleksandr
- Abstract
Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated in the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. Theorems of solvability of the elliptic systems in the extended Sobolev scale are proved. An a priori estimate for solutions is obtained, and their local regularity is studied.
- Subjects
ELLIPTIC functions; SOBOLEV spaces; LINEAR differential equations; SMOOTHNESS of functions; MANIFOLDS (Mathematics); HILBERT space; INTERPOLATION spaces
- Publication
Journal of Mathematical Sciences, 2014, Vol 196, Issue 5, p721
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-014-1688-3