V. N. Los
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A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical
MFAT 26 (2020), no. 2, 111-118
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
MFAT 23 (2017), no. 2, 177-191
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
Valerii Los, Aleksandr A. Murach
MFAT 19 (2013), no. 2, 146-160
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
MFAT 8 (2002), no. 4, 58-71
58-71
