Kasirenko T. Nonregular elliptic boundary-value problems in H?rmander spaces

The thesis elaborates the theory of solvability of general elliptic boundary-value problems in broad classes of the inner product H?rmander spaces and their modifications in the sense of Roitberg. We investigate elliptic problems with boundary conditions of arbitrary orders, which can be greater than or equal to the order of the elliptic equation. We prove theorems on the Fredholm property of the problem under investigation and on some isomorphisms generated by the problem, theorems on a local a priori estimate and the local regularity of its generalized solutions in the Hermander spaces mentioned. As an application, we obtain a sufficient condition under which the generalized partial derivatives (of an arbitrarily chosen order) of the solutions to the problem are continuous and get a new sufficient condition for the generalized solutions to be classical.