Petrovskii elliptic systems in the extended Sobolev scale
Analysis of PDEs
2020-07-28 v1
Abstract
Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. Theorems on the solvability of the elliptic systems on the extended Sobolev scale are proved. An a priori estimate for solutions is obtained, and their regularity is studied.
Keywords
Cite
@article{arxiv.1710.03668,
title = {Petrovskii elliptic systems in the extended Sobolev scale},
author = {Tetiana Zinchenko and Aleksandr Murach},
journal= {arXiv preprint arXiv:1710.03668},
year = {2020}
}
Comments
13 pages; in Russian. English translation is published in J. Math. Sci. (N.Y.) 196 (2014), no. 5, 721-732