Finite local propagation rate of a~hyperbolic equation in the problem of selfadjointness of powers of a~second order elliptic differential operator

Yu. B. Orochko

Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 277-290

Résumé

Let $S$ be a formally selfadjoint second order elliptic expression and $H$ the minimal nonclosed operator in $L_2(\mathbf R^m)$, $m\geqslant1$, generated by it. The property of finite local propagation rate of the hyperbolic equation $\frac{\partial^2u}{\partial t^2}+S[u]=0$ is applied to obtain new criteria for the essential selfadjointness of $H$ and its powers. In these criteria restrictions are imposed on the coefficients of $S$ along a sequence of nonintersecting solid layers diverging to infinity. Bibliography: 17 titles.