On non-closure of range of values of elliptic operator for a plane angle

Let {Mathematical expression} a plane angle of opening α∈(π, 2π). Let PD and PN the Dirichlet and Neumann problems associated to the Poisson equation in {Mathematical expression}. For PD and PN it is proved non existence of solution in Lp ( {Mathematical expression}) when p=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated to PD and PN are not-closed in Lp ( {Mathematical expression}) for p=2/(1±π/α). © 1993 Università degli Studi di Ferrara.