Anop A. V.
Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 299-317
We study nonregular elliptic problems with boundary conditions of higher orders and prove that these problems are Fredholm on appropriate pairs of the inner-product H¨ormander spaces that form a two-sided refined Sobolev scale. We prove a theorem on the regularity of generalized solutions to the problems in these spaces.
Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 867–883
We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean C ∞- domain. It is shown that the operator of the problem is bounded and Fredholm in appropriate pairs of Hörmander inner-product spaces. They are parametrized with the help of an arbitrary radial function RO-varying at ∞ and form the extended Sobolev scale. We establish a priori estimates for the solutions of the problem and study their local regularity on this scale. New sufficient conditions for the generalized partial derivatives of the solutions to be continuous are obtained.