  We investigate an arbitrary regular elliptic boundary-value problem given in
a bounded Euclidean domain with infinitely smooth boundary. We prove that the
operator of the problem is bounded and Fredholm in appropriate pairs of
H\"ormander inner product spaces. They are parametrized with the help of an
arbitrary radial function RO-varying at infinity and form the extended Sobolev
scale. We establish a priori estimates for solutions to the problem and
investigate their local regularity on this scale. We find new sufficient
conditions for generalized partial derivatives of the solutions to be
continuous.
