13 citations · 13 across the 4 of their papers we have counts for
7 papers
Regularity conditions for solutions to some parabolic systems
Oleksandr Diachenko, Valerii Los
We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Result…
A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical
Valerii Los
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 cla…
Parabolic problems in generalized Sobolev spaces
Valerii Los, Vladimir Mikhailets, Aleksandr Murach
We consider a general inhomogeneous parabolic initial-boundary value problem for a -parabolic differential equation given in a finite multidimensional cylinder. We investigate…
General parabolic initial-boundary value problems in Hörmander spaces
V. M. Los, V. A. Mikhailets, A. A. Murach
We investigate a general nonhomogeneous parabolic initial-boundary value problem in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to th…
An isomorphism theorem for parabolic problems in Hörmander spaces and its applications
Valerii Los, Vladimir A. Mikhailets, Aleksandr A. Murach
We investigate a general parabolic initial-boundary value problem with zero Cauchy data in some anisotropic Hörmander inner product spaces. We prove that the operators correspondin…
Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
Valerii Los, Aleksandr Murach
In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a gener…
Parabolic problems and interpolation with a function parameter
Valerii Los, Aleksandr A. Murach
We give an application of interpolation with a function parameter to parabolic differential operators. We introduce the refined anisotropic Sobolev scale that consists of some Hilb…