# V. N. Los

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Articles: 4

### A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical

Valerii Los

Methods Funct. Anal. Topology 26 (2020), no. 2, 111-118

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 classical. The condition is formulated in terms of the belonging of the right-hand sides of the problem to some anisotropic Hörmander spaces.

### Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces

Valerii Los

Methods Funct. Anal. Topology 23 (2017), no. 2, 177-191

We investigate a general nonhomogeneous initial-boundary value problem for a two-dimensional parabolic equation in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hörmander spaces.

### Parabolic problems and interpolation with a function parameter

Methods Funct. Anal. Topology 19 (2013), no. 2, 146-160

We give an application of interpolation with a function parameter to parabolic differential operators. We introduce a refined anisotropic Sobolev scale that consists of some Hilbert function spaces of generalized smoothness. The latter is characterized by a real number and a function varying slowly at infinity in Karamata's sense. This scale is connected with anisotropic Sobolev spaces by means of interpolation with a function parameter. We investigate a general initial--boundary value parabolic problem in the refined Sobolev scale. We prove that the operator corresponding to this problem sets isomorphisms between appropriate spaces pertaining to this scale.

### Sobolev's problem for general elliptic systems of Lere-Volevich's structure

V. N. Los

Methods Funct. Anal. Topology 8 (2002), no. 4, 58-71