On Strong Stability of Classes of Solutions to Elliptic Systei of Linear Partial Differential Equations

摘要

In this article, we study a new (and, to some extent, surprising) phenomenon in the theory of stability of classes of solutions to elliptic systems of linear partial differential equations, namely, the effect of strong stability in the C'-norm. The effect is as follows. Let D be a trivial (see Definition 2) differential operator of form (1) with constant coefficients. Then, for a sufficiently smallE (>0), every Wh]oc-solution to differential inequality (3) is a solution to the system Dg(x) = 0 of partial differential equations. Moreover, for the strong stability of the class of solutions to system (2), the triviality of D is not only sufficient but also necessary.