\(\xi\)-stability of classes of mappings and systems of linear partial differential equations (Q1077617)

In relation with the systems of Moisil-Teodorescu the authors continue the study of \(\xi\)-stability of mapping classes. This notion has been introduced by the second author [Sib. Math. J. 23, 203-224 (1982); translation from Sib. Mat. Zh. 23, No.2, 83-111 (1982; Zbl 0509.32012)]. The main result obtained is that the study of \(\xi\)-stability of a class of solutions of a system of linear partial differential equations with constant coefficients can be reduced to the solution of the same problem for a system having the special form: \[ \sum^{m}_{s=1}\sum^{n}_{i=1}\gamma^ j_{si} \partial g_ s/\partial x_ i=0,\quad j=1,...,k. \] For this particular system a class of solutions is \(\xi\)-stable if and only if the system is elliptic in a special sense.