English

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

R2 v1 2026-06-22T22:09:01.476Z