LAUSR

In a class of inner-product Hörmander spaces, we study a general elliptic problem for which the maximum order of boundary conditions is not lower than the order of the elliptic equation. The role of the order of regularity for these spaces is played by an arbitrary radial positive function RO-varying at infinity in a sense of Avakumović. We prove that the operator of the problem under investigation is bounded and Fredholm in the appropriate pairs of the indicated Hörmander spaces. A theorem on isomorphism generated by this operator is proved. For the generalized solutions of this problem, we establish a local a priori estimate and prove a theorem on the local regularity of these solutions in Hörmander spaces. As an application, we establish new sufficient conditions of continuity for given generalized derivatives of the solutions.