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.
Key words: Parabolic initial-boundary value problem, Hörmander space, slowly varying function, isomorphism property, interpolation with a function parameter.
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Title
Initial-boundary value problems for two-dimensional
parabolic equations in Hörmander spaces