Elliptic problems with boundary conditions of high orders in Hörmander spaces

In a class of inner product Hörmander spaces, we investigate a general elliptic problem for which the maximum of orders of boundary conditions is grater than or equal to the order of elliptic equation. The order of regularity for these spaces is an arbitrary radial positive function RO-varying at infinity in the sense of Avakumović. We prove that the operator of the problem under investigation is bounded and Fredholm on appropriate pairs of Hörmander spaces indicated. A theorem on isomorphism generated by this operator is proved. For generalized solutions to this problem, we establish a local a priory estimate and prove a theorem about their local regularity in Hörmander spaces. As application, we obtain new sufficient conditions under which given derivatives of the solutions are continuous.

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