About the spectrum of the Laplace operator

The famous French scientist J. Hadamard constructed the well-known example illustrating the incorrectness of the Cauchy problem for the Laplace equation. Since then, the question arises whether there exists a Volterra problem for the Laplace equation. In this paper we prove a theorem for a wide class of correct restrictions of the maximal operator $\widehat L$ and the correct extensions of the minimal operator $L_0$, generated by the Laplace operator, which are not Volterra problems.