Quasi-elliptic and weakly coercive systems in Sobolev spaces of vector functions

The purpose of this paper is to investigate a connection between l-quasi-ellipticity and weak coercivity of systems acting on the spaces of vector functions Π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ W_p^{l^{(k)} } $$\end{document} (ℝn). Moreover, we extend some of our earlier results to the matrix case. We also show that an l-quasielliptic system in the sense of O. V. Besov is q-quasi-elliptic in the sense of L. R. Volevich.