On some properties of the set of boundary value problems

For linear differential operations the author studies the connection between the general notion of a correctly posed boundary value problem, given by Hörmander, and its description in terms of the boundary conditions. It is shown that, knowing one correctly posed problem and the kernels of operators that are maximal for the original and adjoint operation, it is possible to describe all correctly posed problems. Examples of explicit realization of this construction are presented. For operators with constant coefficients in a compact domain the author establishes the existence of correctly posed problems with poor regularity properties for the solutions, as well as problems in whose graph there is no dense set of infinitely differentiable functions.
Bibliography: 8 titles.