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In a class of inner product H\"ormander spaces, we investigate a generalelliptic problem for which the maximum of orders of boundary conditions isgrater than or equal to the order of elliptic equation. The order of regularityfor these spaces is an arbitrary radial positive function RO-varying atinfinity in the sense of Avakumovi\'c. We prove that the operator of theproblem under investigation is bounded and Fredholm on appropriate pairs ofH\"ormander spaces indicated. A theorem on isomorphism generated by thisoperator is proved. For generalized solutions to this problem, we establish alocal a priory estimate and prove a theorem about their local regularity inH\"ormander spaces. As application, we obtain new sufficient conditions underwhich given derivatives of the solutions are continuous.

Elliptic problems with boundary conditions of high orders in H\"ormander spaces