  We investigate elliptic boundary-value problems with additional unknown
functions on the boundary of a Euclidean domain. These problems were introduced
by Lawruk. We prove that the operator corresponding to such a problem is
bounded and Fredholm on two-sided refined scales built on the base of the
isotropic H\"ormander inner product spaces. The regularity of the distributions
forming these spaces are characterized by a real number and an arbitrary
function that varies slowly at infinity in the sense of Karamata. For the
generalized solutions to the problem, we prove theorems on a priori estimates
and local regularity in these scales. As applications, we find new sufficient
conditions under which the solutions have continuous classical derivatives of a
prescribed order.
