In analogy with the definition of “extended Sobolev scale" on R n by Mikhailets and Murach,
working in the setting of the lattice Z n, we define the “extended Sobolev scale" H φ (Z n) …

We consider an inhomogeneous initial-boundary value problem for a Petrovskii parabolic
system of second order PDEs. We prove that this problem induces isomorphisms between …

We obtain a new sufficient condition under which generalized solutions to a parabolic initial-
boundary-value problem for a Petrovskii system and the homogeneous Cauchy data are …

The paper contains a survey of the results obtained during the last ten years in the theory of
elliptic boundary problems in H\" ormander function spaces, developed by the authors, and …

The research monograph expounds the foundation of a new theory of parabolic initial-
boundary-value problems in scales of generalized anisotropic Sobolev spaces. These …

We study the properties of global and local regularity of generalized solutions to the
parabolic initial-boundary-value problem for the Petrovskii system of second-order …

We study a parabolic initial-boundary-value problem for a system of two differential
equations with two boundary conditions of different orders, the Dirichlet and Neumann ones …

We investigate global and local regularity of generalized solutions to parabolic initial-
boundary value problem for Petrovskii system of second order differential equations. Results …

We present a survey of the results obtained for the last ten years in the theory of elliptic
boundary-value problems in the Hörmander function spaces developed by the authors, and …

We investigate global and local regularity of generalized solutions to parabolic initial-
boundary value problem for Petrovskii system of second order differential equations. Results …